Answer
$\dfrac{x}{x^{2}-1}-\dfrac{2}{x^{2}-2x+1}=\dfrac{x^{2}-3x-2}{(x+1)(x-1)^{2}}$
Work Step by Step
$\dfrac{x}{x^{2}-1}-\dfrac{2}{x^{2}-2x+1}$
Factor both rational expressions completely:
$\dfrac{x}{x^{2}-1}-\dfrac{2}{x^{2}-2x+1}=\dfrac{x}{(x-1)(x+1)}-\dfrac{2}{(x-1)^{2}}=...$
Evaluate the substraction of the two rational expressions and simplify:
$...=\dfrac{x(x-1)-2(x+1)}{(x+1)(x-1)^{2}}=\dfrac{x^{2}-x-2x-2}{(x+1)(x-1)^{2}}=...$
$...=\dfrac{x^{2}-3x-2}{(x+1)(x-1)^{2}}$