Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
log(x + 1)      x       log(x - 1)
---------- - -------- - ----------
    4           2           4     
             2*x  - 2
(−x2x2−2+log⁡(x+1)4)−log⁡(x−1)4\left(- \frac{x}{2 x^{2} - 2} + \frac{\log{\left(x + 1 \right)}}{4}\right) - \frac{\log{\left(x - 1 \right)}}{4} 
log(x + 1)/4 - x/(2*x^2 - 2) - log(x - 1)/4
Simplificación general [src] 
       /      2\                            
-2*x + \-1 + x /*(-log(-1 + x) + log(1 + x))
--------------------------------------------
                  /      2\                 
                4*\-1 + x /
−2x+(x2−1)(−log⁡(x−1)+log⁡(x+1))4(x2−1)\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))
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)
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)
−x2log⁡(x−1)+x2log⁡(x+1)−2x+log⁡(x−1)−log⁡(x+1)4(x−1)(x+1)\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
−x2log⁡(x−1)+x2log⁡(x+1)−2x+log⁡(x−1)−log⁡(x+1)4x2−4\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)
Denominador común [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
−x2x2−2−log⁡(x−1)4+log⁡(x+1)4- \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)
Unión de expresiones racionales [src] 
       /      2\              /      2\            
-2*x + \-1 + x /*log(1 + x) - \-1 + x /*log(-1 + x)
---------------------------------------------------
                      /      2\                    
                    4*\-1 + x /
−2x−(x2−1)log⁡(x−1)+(x2−1)log⁡(x+1)4(x2−1)\frac{- 2 x - \left(x^{2} - 1\right) \log{\left(x - 1 \right)} + \left(x^{2} - 1\right) \log{\left(x + 1 \right)}}{4 \left(x^{2} - 1\right)} 
(-2*x + (-1 + x^2)*log(1 + x) - (-1 + x^2)*log(-1 + x))/(4*(-1 + x^2))
Potencias [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
−x2x2−2−log⁡(x−1)4+log⁡(x+1)4- \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
−x2x2−2−log⁡(x−1)4+log⁡(x+1)4- \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)
Parte trigonométrica [src] 
  log(-1 + x)   log(1 + x)       x    
- ----------- + ---------- - ---------
       4            4                2
                             -2 + 2*x
−x2x2−2−log⁡(x−1)4+log⁡(x+1)4- \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)
    © Sr Examen – Калькулятор