#### Answer

$\dfrac{x^{2}+9x+20}{x^{2}-25}\cdot\dfrac{x^{2}-9x+20}{x^{2}+8x+16}=\dfrac{x-4}{x+4}$

#### Work Step by Step

$\dfrac{x^{2}+9x+20}{x^{2}-25}\cdot\dfrac{x^{2}-9x+20}{x^{2}+8x+16}$
Factor both rational expressions completely:
$\dfrac{(x+5)(x+4)}{(x-5)(x+5)}\cdot\dfrac{(x-5)(x-4)}{(x+4)^{2}}=...$
Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator:
$...=\dfrac{(x+5)(x+4)(x-5)(x-4)}{(x-5)(x+5)(x+4)^{2}}=\dfrac{x-4}{x+4}$