Answer
$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}=-\dfrac{x}{x-1}$
Work Step by Step
$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}$
Factor the denominator of the first fraction and simplify only the first fraction:
$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}=\dfrac{x-1}{(x-1)^{2}}-\dfrac{x+1}{x-1}=...$
$...=\dfrac{1}{x-1}-\dfrac{x+1}{x-1}=...$
Evaluate the substraction and simplify if possible:
$...=\dfrac{1-x-1}{x-1}=-\dfrac{x}{x-1}$
