## Algebra: A Combined Approach (4th Edition)

$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}=-\dfrac{x}{x-1}$
$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}$ 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: $...=\dfrac{1-x-1}{x-1}=-\dfrac{x}{x-1}$