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Simplificación de expresiones/ Descomposición en fracciones simples/ Abs((x-3)*(x+7))/(((x-3)*(x+7)))+Abs((x-6)*(x+5))/(((x-6)*(x+5)))

¿Cómo vas a descomponer esta Abs((x-3)*(x+7))/(((x-3)*(x+7)))+Abs((x-6)*(x+5))/(((x-6)*(x+5))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
|(x - 3)*(x + 7)|   |(x - 6)*(x + 5)|
----------------- + -----------------
 (x - 3)*(x + 7)     (x - 6)*(x + 5)
∣(x−3)(x+7)∣(x−3)(x+7)+∣(x−6)(x+5)∣(x−6)(x+5)\frac{\left|{\left(x - 3\right) \left(x + 7\right)}\right|}{\left(x - 3\right) \left(x + 7\right)} + \frac{\left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x + 5\right)} 
Abs((x - 3)*(x + 7))/(((x - 3)*(x + 7))) + Abs((x - 6)*(x + 5))/(((x - 6)*(x + 5)))
Simplificación general [src] 
(-6 + x)*(5 + x)*|(-3 + x)*(7 + x)| + (-3 + x)*(7 + x)*|(-6 + x)*(5 + x)|
-------------------------------------------------------------------------
                    (-6 + x)*(-3 + x)*(5 + x)*(7 + x)
(x−6)(x+5)∣(x−3)(x+7)∣+(x−3)(x+7)∣(x−6)(x+5)∣(x−6)(x−3)(x+5)(x+7)\frac{\left(x - 6\right) \left(x + 5\right) \left|{\left(x - 3\right) \left(x + 7\right)}\right| + \left(x - 3\right) \left(x + 7\right) \left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)} 
((-6 + x)*(5 + x)*Abs((-3 + x)*(7 + x)) + (-3 + x)*(7 + x)*Abs((-6 + x)*(5 + x)))/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Respuesta numérica [src] 
Abs((x - 6)*(x + 5))/((5.0 + x)*(-6.0 + x)) + Abs((x - 3)*(x + 7))/((7.0 + x)*(-3.0 + x))
Abs((x - 6)*(x + 5))/((5.0 + x)*(-6.0 + x)) + Abs((x - 3)*(x + 7))/((7.0 + x)*(-3.0 + x))
Unión de expresiones racionales [src] 
(-6 + x)*(5 + x)*|(-3 + x)*(7 + x)| + (-3 + x)*(7 + x)*|(-6 + x)*(5 + x)|
-------------------------------------------------------------------------
                    (-6 + x)*(-3 + x)*(5 + x)*(7 + x)
(x−6)(x+5)∣(x−3)(x+7)∣+(x−3)(x+7)∣(x−6)(x+5)∣(x−6)(x−3)(x+5)(x+7)\frac{\left(x - 6\right) \left(x + 5\right) \left|{\left(x - 3\right) \left(x + 7\right)}\right| + \left(x - 3\right) \left(x + 7\right) \left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)} 
((-6 + x)*(5 + x)*Abs((-3 + x)*(7 + x)) + (-3 + x)*(7 + x)*Abs((-6 + x)*(5 + x)))/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Combinatoria [src] 
     |       2      |      |          2|    2 |       2      |    2 |          2|     |       2      |       |          2|
- 30*|-21 + x  + 4*x| - 21*|30 + x - x | + x *|-21 + x  + 4*x| + x *|30 + x - x | - x*|-21 + x  + 4*x| + 4*x*|30 + x - x |
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                                            (-6 + x)*(-3 + x)*(5 + x)*(7 + x)
x2∣−x2+x+30∣+x2∣x2+4x−21∣+4x∣−x2+x+30∣−x∣x2+4x−21∣−21∣−x2+x+30∣−30∣x2+4x−21∣(x−6)(x−3)(x+5)(x+7)\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)} 
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Denominador racional [src] 
     |       2      |      |          2|    2 |       2      |    2 |          2|     |       2      |       |          2|
- 30*|-21 + x  + 4*x| - 21*|30 + x - x | + x *|-21 + x  + 4*x| + x *|30 + x - x | - x*|-21 + x  + 4*x| + 4*x*|30 + x - x |
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                                            (-6 + x)*(-3 + x)*(5 + x)*(7 + x)
x2∣−x2+x+30∣+x2∣x2+4x−21∣+4x∣−x2+x+30∣−x∣x2+4x−21∣−21∣−x2+x+30∣−30∣x2+4x−21∣(x−6)(x−3)(x+5)(x+7)\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)} 
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Denominador común [src] 
     |       2      |      |          2|    2 |       2      |    2 |          2|     |       2      |       |          2|
- 30*|-21 + x  + 4*x| - 21*|30 + x - x | + x *|-21 + x  + 4*x| + x *|30 + x - x | - x*|-21 + x  + 4*x| + 4*x*|30 + x - x |
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                                                     4              2      3                                              
                                              630 + x  - 99*x - 55*x  + 3*x
x2∣−x2+x+30∣+x2∣x2+4x−21∣+4x∣−x2+x+30∣−x∣x2+4x−21∣−21∣−x2+x+30∣−30∣x2+4x−21∣x4+3x3−55x2−99x+630\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{x^{4} + 3 x^{3} - 55 x^{2} - 99 x + 630} 
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/(630 + x^4 - 99*x - 55*x^2 + 3*x^3)
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