Answer
$\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}=\dfrac{(a+3)(a+5)}{(a+1)(a+2)}$
Work Step by Step
$\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}$
Factor both rational expressions completely:
$\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}=\dfrac{(a+4)(a+3)}{(a+3)(a+2)}\cdot\dfrac{(a+5)(a+3)}{(a+4)(a+1)}$
Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator:
$...=\dfrac{(a+4)(a+3)^{2}(a+5)}{(a+1)(a+2)(a+3)(a+4)}=\dfrac{(a+3)(a+5)}{(a+1)(a+2)}$
