3. Ecuaciones y sistemas de ecuaciones EySE. C1. S06. a. LS. 1er grado. Resolver (algebraica): Ecuación fraccionaria algebraica con denominador numérico Al resolver la ecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#d0«/mi»«mfrac»«mrow»«mo»(«/mo»«mi»#a1«/mi»«mi»#d1«/mi»«mi»#x1«/mi»«mo»)«/mo»«/mrow»«mi»#e1«/mi»«/mfrac»«mi»#d3«/mi»«mfrac»«mrow»«mo»(«/mo»«mi»#a3«/mi»«mi»#x1«/mi»«mi»#d4«/mi»«mi»#b1«/mi»«mo»)«/mo»«/mrow»«mi»#e2«/mi»«/mfrac»«mo»=«/mo»«mi»#a6«/mi»«mi»#d6«/mi»«mfrac»«mrow»«mo»(«/mo»«mi»#x1«/mi»«mi»#d7«/mi»«mi»#b2«/mi»«mo»)«/mo»«/mrow»«mi»#e3«/mi»«/mfrac»«/math»

 

Observación:

- Si el resultado no es entero ingrésalo como fracción de la forma a/b o -a/b.

 

El resultado corresponde a:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x1«/mi»«mo»=«/mo»«/math» {#1}

 

]]> Lo primero que debemos hacer es multiplicar a ambos lados de la igualdad por el mínimo común múltiplo de los denominadores,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mtable»«mtr»«mtd»«mi»#d0«/mi»«mfrac»«mrow»«mi»#a1«/mi»«mi»#d1«/mi»«mi»#x1«/mi»«/mrow»«mi»#e1«/mi»«/mfrac»«mi»#d3«/mi»«mfrac»«mrow»«mi»#a3«/mi»«mi»#x1«/mi»«mi»#d4«/mi»«mi»#b1«/mi»«/mrow»«mi»#e2«/mi»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#a6«/mi»«mi»#d6«/mi»«mfrac»«mrow»«mi»#x1«/mi»«mi»#d7«/mi»«mi»#b2«/mi»«/mrow»«mi»#e3«/mi»«/mfrac»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»/«/mo»«/mtd»«mtd»«mi»#z20«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#d0«/mi»«mi»#f1«/mi»«mfenced»«mrow»«mi»#a1«/mi»«mi»#d1«/mi»«mi»#x1«/mi»«/mrow»«/mfenced»«mi»#d3«/mi»«mi»#f2«/mi»«mfenced»«mrow»«mi»#a3«/mi»«mi»#x1«/mi»«mi»#d4«/mi»«mi»#b1«/mi»«/mrow»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#f3«/mi»«mi»#d6«/mi»«mi»#f4«/mi»«mfenced»«mrow»«mi»#x1«/mi»«mi»#d7«/mi»«mi»#b2«/mi»«/mrow»«/mfenced»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»
 
 
Luego, aplicamos propiedad distributiva y sumamos términos semejantes

 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f5«/mi»«mi»#d8«/mi»«mi»#f6«/mi»«mi»#x1«/mi»«mo»=«/mo»«mi»#f7«/mi»«mi»#d6«/mi»«mi»#f4«/mi»«mi»#x1«/mi»«/math»
 
 

Posteriormente, sumamos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#g1«/mi»«/math» y sumamos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#g2«/mi»«mi»#x1«/mi»«/math» a ambos lados de la igualdad,


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mtable»«mtr»«mtd»«mi»#f5«/mi»«mi»#d8«/mi»«mi»#f6«/mi»«mi»#x1«/mi»«mi»#d10«/mi»«mi»#f8«/mi»«mi»#d11«/mi»«mi»#f9«/mi»«mi»#x1«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#f7«/mi»«mi»#d6«/mi»«mi»#f4«/mi»«mi»#x1«/mi»«mi»#d10«/mi»«mi»#f8«/mi»«mi»#d11«/mi»«mi»#f9«/mi»«mi»#x1«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»#z22«/mi»«mi»#x1«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#z21«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»/«/mo»«/mtd»«mtd»«mfenced»«mfrac»«mn»1«/mn»«mi»#z22«/mi»«/mfrac»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi»#x1«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»#z21«/mi»«/mrow»«mi»#z22«/mi»«/mfrac»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»#x1«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#sol«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»
 
 
Por lo tanto:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x1«/mi»«mo»=«/mo»«mi»#sol«/mi»«/math»

 

 

 

Reporta y/o califica esta pregunta:

1. Copia este código: EySE. C1. S06. a. LS.

2. Presiona este enlace, pega el código y completa el formulario

 

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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mrow><mi>mcm</mi><mfenced><mrow><mi>a2</mi><mo>,</mo><mi>a5</mi><mo>,</mo><mi>a8</mi></mrow></mfenced></mrow><mi>a8</mi></mfrac><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>d11</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>d11</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mo>-</mo><mi>f5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>mcm</mi><mfenced><mrow><mi>a2</mi><mo>,</mo><mi>a5</mi><mo>,</mo><mi>a8</mi></mrow></mfenced></mrow><mi>a8</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>mcm</mi><mfenced><mrow><mi>e1</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mi>e3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><mfrac><mi>g3</mi><mi>a2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g5</mi><mo>=</mo><mfrac><mi>g3</mi><mi>a5</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g6</mi><mo>=</mo><mfrac><mi>g3</mi><mi>a8</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g7</mi><mo>=</mo><mi>g4</mi><mo>*</mo><mi>c1</mi><mo>+</mo><mi>g5</mi><mo>*</mo><mi>a3</mi><mo>-</mo><mi>g6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g8</mi><mo>=</mo><mi>f1</mi><mo>*</mo><mi>c1</mi><mo>+</mo><mi>f2</mi><mo>*</mo><mi>a3</mi><mo>+</mo><mfrac><mrow><mi>mcm</mi><mfenced><mrow><mi>a2</mi><mo>,</mo><mi>a5</mi><mo>,</mo><mi>a8</mi></mrow></mfenced></mrow><mi>a8</mi></mfrac></math></input></command></group></library><group><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><mfrac><mn>19</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><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="casSession"/></localData></question>