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Simplificación de expresiones/ Descomposición en fracciones simples/ ((x+1)^2/(x-1)^2)*(x-1)*(2/(x-1)-2*(x+1)/(x-1)^2)/(x+1)

¿Cómo vas a descomponer esta ((x+1)^2/(x-1)^2)*(x-1)*(2/(x-1)-2*(x+1)/(x-1)^2)/(x+1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       2                            
(x + 1)          /  2     2*(x + 1)\
--------*(x - 1)*|----- - ---------|
       2         |x - 1           2|
(x - 1)          \         (x - 1) /
------------------------------------
               x + 1
(x+1)2(x−1)2(x−1)(−2(x+1)(x−1)2+2x−1)x+1\frac{\frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}} \left(x - 1\right) \left(- \frac{2 \left(x + 1\right)}{\left(x - 1\right)^{2}} + \frac{2}{x - 1}\right)}{x + 1} 
((((x + 1)^2/(x - 1)^2)*(x - 1))*(2/(x - 1) - 2*(x + 1)/(x - 1)^2))/(x + 1)
Descomposición de una fracción [src] 
-8/(-1 + x)^3 - 4/(-1 + x)^2
−4(x−1)2−8(x−1)3- \frac{4}{\left(x - 1\right)^{2}} - \frac{8}{\left(x - 1\right)^{3}} 
      8           4    
- --------- - ---------
          3           2
  (-1 + x)    (-1 + x)
Simplificación general [src] 
-(4 + 4*x) 
-----------
         3 
 (-1 + x)
−4x+4(x−1)3- \frac{4 x + 4}{\left(x - 1\right)^{3}} 
-(4 + 4*x)/(-1 + x)^3
Compilar la expresión [src] 
        /  2       2 + 2*x \
(1 + x)*|------ - ---------|
        |-1 + x           2|
        \         (-1 + x) /
----------------------------
           -1 + x
(x+1)(2x−1−2x+2(x−1)2)x−1\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1} 
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Parte trigonométrica [src] 
        /  2       2 + 2*x \
(1 + x)*|------ - ---------|
        |-1 + x           2|
        \         (-1 + x) /
----------------------------
           -1 + x
(x+1)(2x−1−2x+2(x−1)2)x−1\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1} 
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Unión de expresiones racionales [src] 
-4*(1 + x)
----------
        3 
(-1 + x)
−4(x+1)(x−1)3- \frac{4 \left(x + 1\right)}{\left(x - 1\right)^{3}} 
-4*(1 + x)/(-1 + x)^3
Combinatoria [src] 
-4*(1 + x)
----------
        3 
(-1 + x)
−4(x+1)(x−1)3- \frac{4 \left(x + 1\right)}{\left(x - 1\right)^{3}} 
-4*(1 + x)/(-1 + x)^3
Potencias [src] 
        /  2       -2 - 2*x\
(1 + x)*|------ + ---------|
        |-1 + x           2|
        \         (-1 + x) /
----------------------------
           -1 + x
(x+1)(−2x−2(x−1)2+2x−1)x−1\frac{\left(x + 1\right) \left(\frac{- 2 x - 2}{\left(x - 1\right)^{2}} + \frac{2}{x - 1}\right)}{x - 1} 
        /  2       2 + 2*x \
(1 + x)*|------ - ---------|
        |-1 + x           2|
        \         (-1 + x) /
----------------------------
           -1 + x
(x+1)(2x−1−2x+2(x−1)2)x−1\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1} 
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Denominador común [src] 
    -(4 + 4*x)      
--------------------
      3      2      
-1 + x  - 3*x  + 3*x
−4x+4x3−3x2+3x−1- \frac{4 x + 4}{x^{3} - 3 x^{2} + 3 x - 1} 
-(4 + 4*x)/(-1 + x^3 - 3*x^2 + 3*x)
Denominador racional [src] 
        /          2                      \
(1 + x)*\2*(-1 + x)  + (-1 + x)*(-2 - 2*x)/
-------------------------------------------
                         4                 
                 (-1 + x)
(x+1)((−2x−2)(x−1)+2(x−1)2)(x−1)4\frac{\left(x + 1\right) \left(\left(- 2 x - 2\right) \left(x - 1\right) + 2 \left(x - 1\right)^{2}\right)}{\left(x - 1\right)^{4}} 
(1 + x)*(2*(-1 + x)^2 + (-1 + x)*(-2 - 2*x))/(-1 + x)^4
Respuesta numérica [src] 
(1.0 + x)*(2.0/(-1.0 + x) - (2.0 + 2.0*x)/(-1.0 + x)^2)/(-1.0 + x)
(1.0 + x)*(2.0/(-1.0 + x) - (2.0 + 2.0*x)/(-1.0 + x)^2)/(-1.0 + x)
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