1rBTX 04. FUNCIONS/1.4.2 Operacions amb funcions 1.4.2.11Q SumaFuncRacionalsG1G1 Quina és la funció suma de les funcions:

«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¨»§#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¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»?«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mrow»«mn»2«/mn»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/mstyle»«/math» Pots deixar el denominador factoritzat

]]> Resultat correcte: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«/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>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c4</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>c5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c6</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>c7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c8</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>c1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>c3</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c4</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>c5</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c6</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>c7</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c8</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>c1</mi></mfenced><mo>≠</mo><mfenced close="|" open="|"><mi>c3</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>c2</mi><mo>≠</mo><mi>c4</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>c5</mi></mfenced><mo>≠</mo><mfenced close="|" open="|"><mi>c7</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>c6</mi><mo>≠</mo><mi>c8</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>sol</mi><mo>=</mo><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>M1</mi><mo>=</mo><mi>denominador</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</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>d12</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>mcm</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</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>w2</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>m11</mi><mo>=</mo><mi>factoritza</mi><mfenced><mfrac><mi>d11</mi><mi>d1</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m21</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mfrac><mi>d11</mi><mi>d2</mi></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mfrac><mi>d11</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mfrac><mi>d11</mi><mi>d2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>t1</mi><mo>+</mo><mi>t2</mi></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><mi>x</mi><mo>-</mo><mn>4</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>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>15</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>70</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>110</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>100</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>,</mo><mi>m11</mi><mo>,</mo><mi>m21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>60</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>200</mn><mo>,</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mn>4</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>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>80</mn><mo>,</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>120</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>300</mn><mo>,</mo><mn>22</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>140</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>220</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</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></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> És una suma de fraccions algèbriques.

Calcula el mcm de «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»«/mrow»«/mstyle»«/math» per trobar el denominador comú.

]]> El denominador comú dels denominadors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» és #d12

La suma es transforma en:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

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