Answer
$-\displaystyle \frac{2}{(x-1)(x+1)}$
Work Step by Step
$\displaystyle \frac{2x-3}{x-1}-\frac{2x+1}{x+1}=... \quad LCD=(x-1)(x+1)$
$=\displaystyle \frac{(2x-3)(x+1)-(2x+1)(x-1)}{(x-1)(x+1)}$
$=\displaystyle \frac{(2x^{2}+2x-3x-3)-(2x^{2}-2x+x-1)}{(x-1)(x+1)}$
$=\displaystyle \frac{2x^{2}+2x-3x-3-2x^{2}+2x-x+1}{(x-1)(x+1)}$
$=\displaystyle \frac{-2}{(x-1)(x+1)}$
$=-\displaystyle \frac{2}{(x-1)(x+1)}$
