Answer
$\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}=\dfrac{x-3}{x+2}$
Work Step by Step
$\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}$
Factor the first rational expression completely:
$\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}=\dfrac{(x-3)(x+3)}{(x-2)(x+2)}\cdot\dfrac{x-2}{x+3}=...$
Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{(x-3)(x+3)(x-2)}{(x-2)(x+2)(x+3)}=\dfrac{x-3}{x+2}$
