Solve for: (2)/(x+1)-(x)/(x^2-1)

Expression: $\frac{ 2 }{ x+1 }-\frac{ x }{ {x}^{2}-1 }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

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

Write all numerators above the least common denominator $\left( x-1 \right) \times \left( x+1 \right)$

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

Distribute $2$ through the parentheses

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

Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product

$\frac{ 2x-2-x }{ {x}^{2}-1 }$

Collect like terms

$\frac{ x-2 }{ {x}^{2}-1 }$