4t ESO/4.04 EQUACIONS/4.04.1 Equació 1r grau/4.04.1.5 Treure denominadors 4.04.1.5.11Q Treu2DenominadorsFinsParèntesis Treu els denominadors (fins a parèntesis) de l'equació següent

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mi mathvariant=¨bold¨»#e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»#f«/mi»«/mrow»«mi mathvariant=¨bold¨»#o«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

Format de la resposta 1: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»5«/mn»«mo»§#183;«/mo»«mo»(«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mn»20«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mn»4«/mn»«mo»§#183;«/mo»«mo»(«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mn»20«/mn»«/mfrac»«/mstyle»«/math»

Format de la resposta 2: 5·(2x+1)=10·(3x-1)

NO S'HA DE RESOLDRE! Només cal treure denominadors

Atenció: el denominador comú és el mcm!

]]> Respostes correctes

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_c«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_c«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 resposta 1 =#solresposta 2 =#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</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>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</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>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>e</mi></mrow></apply></math></input></command><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>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>o</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mfenced><mrow><mi>m</mi><mo>≠</mo><mi>o</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>o</mi><mo>)</mo><mo>=</mo><mi>w</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_m</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_m</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_o</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_o</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_c</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>o</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_3</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mi>m_3</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>resol</mi><mo> </mo><mi>equació</mi><mo>(</mo><mi>m_1</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mi>m_3</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>)</mo><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</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>o</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>,</mo><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_m</mi><mo>,</mo><mi>b_m</mi><mo>,</mo><mi>e_o</mi><mo>,</mo><mi>f_o</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>525</mn><mo>,</mo><mn>300</mn><mo>,</mo><mn>270</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>225</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>m_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>5</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"><mo>-</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn><mo>=</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>32</mn><mn>51</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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"><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>a</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>a</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El mínim comú múltiple dels denominadors és #m_c.

Si fem les divisions, els coeficients de cada parèntesis són:

#m_c / #m = #m_1
#m_c / #o = #m_3

El primer pas és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_c«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m_c«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Només cal treure denominadors.

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