Answer
$\dfrac{\dfrac{2x^{2}-3x-2}{x^{2}-1}}{\dfrac{2x^{2}+5x+2}{x^{2}+x-2}}=\dfrac{x-2}{x+1}$
Work Step by Step
$\dfrac{\dfrac{2x^{2}-3x-2}{x^{2}-1}}{\dfrac{2x^{2}+5x+2}{x^{2}+x-2}}$
Factor the expression completely:
$\dfrac{\dfrac{2x^{2}-3x-2}{x^{2}-1}}{\dfrac{2x^{2}+5x+2}{x^{2}+x-2}}=\dfrac{\dfrac{(x-2)(2x+1)}{(x+1)(x-1)}}{\dfrac{(2x+1)(x+2)}{(x-1)(x+2)}}=...$
Evaluate the division:
$...=\dfrac{(x-2)(2x+1)(x-1)(x+2)}{(2x+1)(x+2)(x+1)(x-1)}=...$
Simplify:
$...=\dfrac{x-2}{x+1}$
