Answer
$\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}=\dfrac{(x+2)(x-3)}{(x-4)(x+4)}$
Work Step by Step
$\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}$
Factor both rational expressions completely:
$\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}=\dfrac{(x+4)(x+2)}{(x+5)(x-4)}\cdot\dfrac{(x+5)(x-3)}{(x+4)^{2}}$
Multiply and then simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{(x+4)(x+2)(x+5)(x-3)}{(x+5)(x-4)(x+4)^{2}}=\dfrac{(x+2)(x-3)}{(x-4)(x+4)}$
