Question

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

Answer 1

Respuesta:

saludos

Explicación paso a paso:

Answer 2

Respuesta:

[tex]\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)}}[/tex]

[tex]\mathrm{Factorizar:}[/tex]

[tex]x^2-1=\left(x+1\right)\left(x-1\right)[/tex]

[tex]\mathrm{Eliminamos \ parentesis:}[/tex]

[tex]\frac{1}{x+1}+\frac{2x}{\left(x+1\right)\left(x-1\right)}-\frac{1}{x-1}[/tex]

[tex]\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)}[/tex]

[tex]\mathrm{Combinamos \ fracciones, \ recordando \ que:}[/tex]

[tex]\boxed{\bold{\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}}[/tex]

[tex]\frac{x-1+2x-\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}[/tex]

[tex]\mathrm{Factorizamos:}[/tex]

[tex]x-1+2x-\left(x+1\right)=3x-\left(x+1\right)-1[/tex]

[tex]\frac{3x-\left(x+1\right)-1}{\left(x+1\right)\left(x-1\right)}[/tex]

[tex]3x-\left(x+1\right)-1=2(x-1)[/tex]

[tex]\frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}[/tex]

[tex]\mathrm{Eliminamos \ termino \ comun \ y \ eliminamos \ parentesis :}[/tex]

[tex](\text{x}-1)=\text{x}-1[/tex]

Solución

[tex]\boxed{\frac{2}{\text{x}+1}}[/tex]

Saludos...