Question

1/(x+1)+2x/(x^2-1)-1/(x-1)

Answer 1

Respuesta:

saludos

Explicación paso a paso:

Answer 2

Respuesta:

$\boxed{\frac{1}{\left(\text{x}+1\right)}+\frac{2\text{x}}{\left(\text{x}^2-1\right)}-\frac{1}{\left(\text{x}-1\right)}}$

$\mathrm{Factorizar:}$

$x^2-1=\left(x+1\right)\left(x-1\right)$

$\mathrm{Eliminamos \ parentesis:}$

$\frac{1}{x+1}+\frac{2x}{\left(x+1\right)\left(x-1\right)}-\frac{1}{x-1}$

$\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{2x}{\left(x+1\right)\left(x-1\right)}-\frac{x+1}{\left(x+1\right)\left(x-1\right)}$

$\mathrm{Combinamos \ fracciones, \ recordando \ que:}$

$\boxed{\bold{\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}}$

$\frac{x-1+2x-\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}$

$\mathrm{Factorizamos:}$

$x-1+2x-\left(x+1\right)=3x-\left(x+1\right)-1$

$\frac{3x-\left(x+1\right)-1}{\left(x+1\right)\left(x-1\right)}$

$3x-\left(x+1\right)-1=2(x-1)$

$\frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}$

$\mathrm{Eliminamos \ termino \ comun \ y \ eliminamos \ parentesis :}$

$(\text{x}-1)=\text{x}-1$

Solución

$\boxed{\frac{2}{\text{x}+1}}$

Saludos...