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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x+1)/4-log(x-1)/4-x/(2*x^2-2)

¿Cómo vas a descomponer esta log(x+1)/4-log(x-1)/4-x/(2*x^2-2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
log(x + 1)   log(x - 1)      x    
---------- - ---------- - --------
    4            4           2    
                          2*x  - 2
$$- \frac{x}{2 x^{2} - 2} + \left(- \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right)$$ 
log(x + 1)/4 - log(x - 1)/4 - x/(2*x^2 - 2)
Simplificación general [src] 
       /      2\                            
-2*x + \-1 + x /*(-log(-1 + x) + log(1 + x))
--------------------------------------------
                  /      2\                 
                4*\-1 + x /
$$\frac{- 2 x + \left(x^{2} - 1\right) \left(- \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right)}{4 \left(x^{2} - 1\right)}$$ 
(-2*x + (-1 + x^2)*(-log(-1 + x) + log(1 + x)))/(4*(-1 + x^2))
Denominador común [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
$$- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}$$ 
-log(-1 + x)/4 + log(1 + x)/4 - x/(-2 + 2*x^2)
Combinatoria [src] 
                     2               2                          
-log(1 + x) - 2*x + x *log(1 + x) - x *log(-1 + x) + log(-1 + x)
----------------------------------------------------------------
                       4*(1 + x)*(-1 + x)
$$\frac{- x^{2} \log{\left(x - 1 \right)} + x^{2} \log{\left(x + 1 \right)} - 2 x + \log{\left(x - 1 \right)} - \log{\left(x + 1 \right)}}{4 \left(x - 1\right) \left(x + 1\right)}$$ 
(-log(1 + x) - 2*x + x^2*log(1 + x) - x^2*log(-1 + x) + log(-1 + x))/(4*(1 + x)*(-1 + x))
Denominador racional [src] 
                     2               2                          
-log(1 + x) - 2*x + x *log(1 + x) - x *log(-1 + x) + log(-1 + x)
----------------------------------------------------------------
                                   2                            
                           -4 + 4*x
$$\frac{- x^{2} \log{\left(x - 1 \right)} + x^{2} \log{\left(x + 1 \right)} - 2 x + \log{\left(x - 1 \right)} - \log{\left(x + 1 \right)}}{4 x^{2} - 4}$$ 
(-log(1 + x) - 2*x + x^2*log(1 + x) - x^2*log(-1 + x) + log(-1 + x))/(-4 + 4*x^2)
Unión de expresiones racionales [src] 
       /      2\                            
-2*x + \-1 + x /*(-log(-1 + x) + log(1 + x))
--------------------------------------------
                  /      2\                 
                4*\-1 + x /
$$\frac{- 2 x + \left(x^{2} - 1\right) \left(- \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right)}{4 \left(x^{2} - 1\right)}$$ 
(-2*x + (-1 + x^2)*(-log(-1 + x) + log(1 + x)))/(4*(-1 + x^2))
Parte trigonométrica [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
$$- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}$$ 
-log(-1 + x)/4 + log(1 + x)/4 - x/(-2 + 2*x^2)
Potencias [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
$$- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}$$ 
-log(-1 + x)/4 + log(1 + x)/4 - x/(-2 + 2*x^2)
Compilar la expresión [src] 
  log(x - 1)   log(x + 1)       x    
- ---------- + ---------- - ---------
      4            4                2
                            -2 + 2*x
$$- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}$$ 
-log(x - 1)/4 + log(x + 1)/4 - x/(-2 + 2*x^2)
Respuesta numérica [src] 
0.25*log(x + 1) - 0.25*log(x - 1) - x/(-2.0 + 2.0*x^2)
0.25*log(x + 1) - 0.25*log(x - 1) - x/(-2.0 + 2.0*x^2)
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