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

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

Expresión a simplificar:

Solución

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