1rBTX 02. POLINOMIS/1.2.5 Fraccions algèbriques 1.2.5.10DT SIMPLIFICA FA

Simplifica fraccions algèbriques

Per simplificar fraccions algèbriques, dividim el seu numerador i el seu denominador per el mcd d'ambdós.

A la practica, "tatxem" els factors repetits al numerador i al denominador si TOTS els factors s'estant multiplicant entre ells; MAI si s'estan sumant.

]]> 0.0000000 0.0000000 0 1.2.5.11Q SimplificaFA G3G3 Simplifica la fracció «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/math»

]]> 1.2.5.12Q SimplificaFA G4G4 amb arrel num i den Simplifica la fracció:

sabent que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math» són arrels del numerador i del denominador.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>M</mi></mtd></mtr></mtable></mfenced><mi>N</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><msup><mo>)</mo><mn>2</mn></msup></mrow><mrow><mi>a_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_6</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>256</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>768</mn></mtd></mtr></mtable></mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>114</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>522</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>648</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>64</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>54</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Factoritza el numerador i el denominador:

Ja pots simplificar

]]> 1.2.5.20DT SUMA FA Suma de fraccions algèbriques

Primer cal reduir-les al mínim comú denominador que és el polinomi mcm dels denominadors (Tots els factors amb l'exponent més gran)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»+«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»25«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»=«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»(«/mo»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»x«/mi»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»+«/mo»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»5«/mn»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»(«/mo»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»x«/mi»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»+«/mo»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»5«/mn»«mo mathcolor=¨#0000FF¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»+«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Quan tenen el mateix denominador, es sumen els numeradors.

]]> 0.0000000 0.0000000 0 1.2.5.21Q SumaFA G1G1 Primers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors #d1 i #d2 no tenen cap divisor comú, el mcm per realitzar la suma és (#d1)·(#d2).

L'expressió es transforma en:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Ara ja tenen el mateix denominador i es poden sumar els numeradors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«/math»

]]> 1.2.5.22Q SumaFA G1G1 NoPrimers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_3</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo>≠</mo><mi>b_3</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b_2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></mrow><mrow><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math» són múltiples de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mstyle»«/math»,

el denominador comú per la suma és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«/mrow»«/mstyle»«/math»

L'expressió es transforma en:

Ara ja tenen el mateix denominador i es pot calcular el numerador, multiplicant i sumant.

]]> 1.2.5.23Q SumaFA G1G2 NoPrimers Suma les fraccions: F(x) + G(x)

amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p11</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>p21</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que #d1 = #d11

i que #d2 = #d21,

el mcm dels denominadors és #mc11.

]]> Si el mcm dels denominadors és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=a409f4635fdb01c84b8b95b96ed1568f&cw=46&ch=10&cb=9" style="vertical-align: -1px;"/>, la suma s'escriu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=e99ead11a57c6034b2d2d5fd8c01bfbd&cw=303&ch=27&cb=18" style="vertical-align: -9px;"/>

]]> 1.2.5.24Q SumaFa G1G2 Primers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.2.5.25Q SumaFA G2G2 NoPrimers Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>b_3</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>mcm</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo><mo>,</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d12</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>21</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Les factoritzacions dels denominadors són:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fn«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»fd«/mi»«mspace linebreak=¨newline¨/»«/mrow»«/mstyle»«/math»

el seu mcm, i per tant el denominador comú és:

]]> 1.2.5.26Q SumaFA G2G2 NoPrimers IdRemarcable Suma les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a4</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>b3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a4</mi><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a3</mi><mo>,</mo><mi>b3</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo></mrow><mrow><mi>a3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a4</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>+</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>125</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>125</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>21</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>66</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>45</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>250</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1250</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>250</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1250</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>90</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>75</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»

i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»21«/mn»«/mrow»«/mstyle»«/math»,

el denominador comú és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math».

]]> Si el denominador comú és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mc«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»,

la suma es transforma en:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.2.5.31Q RestaFA G1G1 Primers Resta les fraccions F(x) – G(x)

amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>-</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>b_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els denominadors #d1 i #d2 no tenen cap divisor comú, el mcm per realitzar la suma és (#d1)·(#d2).

L'expressió es transforma en:

Ara ja tenen el mateix denominador i es poden sumar els numeradors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«/mrow»«/mstyle»«/math»

]]> 1.2.5.32Q RestaFA G1G2 NoPrimers Resta les fraccions: F(x) – G(x)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_6</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p11</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>mc1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>p21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>-</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>p21</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que #d1 = #d11

i que #d2 = #d21,

el mcm dels denominadors és #mc11.

]]> Si el mcm dels denominadors és #mc11, la resta s'escriu:

]]> 1.2.5.33Q RestaFA G2G2 NoPrimers Resta les fraccions F(x) – G(x)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_1</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>b_3</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac><mo>≠</mo><mfrac><mi>a_2</mi><mi>a_1</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b_2</mi><mo>≠</mo><mfrac><mi>a_4</mi><mi>a_3</mi></mfrac></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_2</mi><mo>)</mo></mrow><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>a_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a_4</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>F</mi><mo>-</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>mcm</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo><mo>,</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d12</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mi>factoritza</mi><mfenced><mrow><mi>b_1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b_2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Les factoritzacions dels denominadors són:

el seu mcm, i per tant el denominador comú és:

]]> 1.2.5.40DT PRODUCTE FA Multiplicació de fraccions algèbriques

Es presenta el numerador de la 1a multiplicat pel numerador de la 2a i el denominador de la 1a multiplicat pel denominador de la 2a:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»

Es factoritza el numerador i el denominador per simplificar:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.2.5.41Q MultiplicaFA G1G1 Simplificable Multiplica les fraccions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat i factoritzat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>a_2</mi></mrow><mi>f5</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>,</mo><mi>a_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>36</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>36</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>8</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>108</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>144</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>216</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Es fa la multiplicació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

b) Es factoritza el numerador: #f1

es factoritza el denominador: #f2

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

i es simplifica pel seu mcd que és #mc1

]]> 1.2.5.42Q MultiplicaFA G2G2 Simplificable Multiplica les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b6</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>b4</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>b6</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>a2</mi><mo>)</mo></mrow><mrow><mi>b1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>b2</mi><mo>)</mo></mrow><mrow><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b6</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>n3</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>F</mi><mo>*</mo><mi>G</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df3</mi><mo>=</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi><mo>*</mo><mo>(</mo><mi>b4</mi><mo>+</mo><mi>b6</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>b4</mi><mo>*</mo><mi>b6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>factoritza</mi><mfenced><mi>df3</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>a2</mi></mrow><mi>f3</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>28</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>112</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>154</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>280</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df3</mi><mo>,</mo><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn><mo>,</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Es fa la multiplicació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

b) Es factoritza el numerador: #f1

es factoritza el denominador: #f2

i es simplifica pel seu mcd que és #mc1

]]> 1.2.5.50DT DIVISIÓ FA Divisió de fraccions algèbriques

Es multiplica la 1a per la inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»

Es factoritza el numerador i el denominador per simplificar:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.2.5.51Q DivisióFA G1G1 Simplificable Divideix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

Resultat simplificat i factoritzat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>b3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b4</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>b3</mi><mo>,</mo><mi>a4</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b4</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n1</mi><mo>*</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>*</mo><mi>n2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>b3</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>*</mo><mi>b4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a4</mi><mo>*</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n4</mi><mi>d4</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>F</mi><mi>G</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></mrow><mrow><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></mrow><mrow><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es multiplica la primera fracció per la inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»G«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Després es factoritza

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»G«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

i es simplifica

]]> 1.2.5.52Q DivisióFA G2G2 Simplificable Divideix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»amb«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»G«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b5</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a6</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>b4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b5</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b6</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a4</mi><mo>,</mo><mi>b4</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a3</mi><mo>≠</mo><mi>b3</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a3</mi><mo>≠</mo><mi>a6</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b6</mi><mo>≠</mo><mi>b3</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b6</mi><mo>≠</mo><mi>a6</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>n1</mi><mo>*</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>d1</mi><mo>*</mo><mi>n2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n51</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>b4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b6</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n52</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b3</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a6</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n51</mi><mi>n52</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>F</mi><mi>G</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>77</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>126</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>105</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>28</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>84</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>108</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>324</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>65</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>210</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>28</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n51</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es multiplica la primera fracció per la inversa de la segona:

Després es factoritza i es simplifica:

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