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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x+1)/4+(3*log(x-1))/4+3/(2+2*x)

¿Cómo vas a descomponer esta log(x+1)/4+(3*log(x-1))/4+3/(2+2*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
log(x + 1)   3*log(x - 1)      3   
---------- + ------------ + -------
    4             4         2 + 2*x
$$\left(\frac{3 \log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right) + \frac{3}{2 x + 2}$$ 
log(x + 1)/4 + (3*log(x - 1))/4 + 3/(2 + 2*x)
Simplificación general [src] 
6 + (1 + x)*(3*log(-1 + x) + log(1 + x))
----------------------------------------
               4*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right) + 6}{4 \left(x + 1\right)}$$ 
(6 + (1 + x)*(3*log(-1 + x) + log(1 + x)))/(4*(1 + x))
Respuesta numérica [src] 
0.25*log(x + 1) + 0.75*log(x - 1) + 3.0/(2.0 + 2.0*x)
0.25*log(x + 1) + 0.75*log(x - 1) + 3.0/(2.0 + 2.0*x)
Parte trigonométrica [src] 
   3      log(1 + x)   3*log(-1 + x)
------- + ---------- + -------------
2 + 2*x       4              4
$$\frac{3 \log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4} + \frac{3}{2 x + 2}$$ 
3/(2 + 2*x) + log(1 + x)/4 + 3*log(-1 + x)/4
Unión de expresiones racionales [src] 
6 + (1 + x)*(3*log(-1 + x) + log(1 + x))
----------------------------------------
               4*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right) + 6}{4 \left(x + 1\right)}$$ 
(6 + (1 + x)*(3*log(-1 + x) + log(1 + x)))/(4*(1 + x))
Denominador común [src] 
   3      log(1 + x)   3*log(-1 + x)
------- + ---------- + -------------
2 + 2*x       4              4
$$\frac{3 \log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4} + \frac{3}{2 x + 2}$$ 
3/(2 + 2*x) + log(1 + x)/4 + 3*log(-1 + x)/4
Potencias [src] 
   3      log(1 + x)   3*log(-1 + x)
------- + ---------- + -------------
2 + 2*x       4              4
$$\frac{3 \log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4} + \frac{3}{2 x + 2}$$ 
3/(2 + 2*x) + log(1 + x)/4 + 3*log(-1 + x)/4
Combinatoria [src] 
6 + 3*log(-1 + x) + x*log(1 + x) + 3*x*log(-1 + x) + log(1 + x)
---------------------------------------------------------------
                           4*(1 + x)
$$\frac{3 x \log{\left(x - 1 \right)} + x \log{\left(x + 1 \right)} + 3 \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)} + 6}{4 \left(x + 1\right)}$$ 
(6 + 3*log(-1 + x) + x*log(1 + x) + 3*x*log(-1 + x) + log(1 + x))/(4*(1 + x))
Denominador racional [src] 
6 + 3*log(-1 + x) + x*log(1 + x) + 3*x*log(-1 + x) + log(1 + x)
---------------------------------------------------------------
                            4 + 4*x
$$\frac{3 x \log{\left(x - 1 \right)} + x \log{\left(x + 1 \right)} + 3 \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)} + 6}{4 x + 4}$$ 
(6 + 3*log(-1 + x) + x*log(1 + x) + 3*x*log(-1 + x) + log(1 + x))/(4 + 4*x)
Compilar la expresión [src] 
   3      log(x + 1)   3*log(x - 1)
------- + ---------- + ------------
2 + 2*x       4             4
$$\frac{3 \log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4} + \frac{3}{2 x + 2}$$ 
3/(2 + 2*x) + log(x + 1)/4 + 3*log(x - 1)/4
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