Answer
$\color{blue}{\dfrac{a+4}{a-3}}$
Work Step by Step
Use the rule $\dfrac{a}{b} \div \dfrac{c}{d}= \dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain:
$=\dfrac{4a+12}{2a-10} \cdot \dfrac{a^2-a-20}{a^2-9}$
Factor each polynomial, then cancel common factors to obtain:
$\require{cancel}
=\dfrac{4(a+3)}{2(a-5)} \cdot \dfrac{(a-5)(a+4)}{(a-3)(a+3)}
\\=\dfrac{\cancel{4}2\cancel{(a+3)}}{\cancel{2}\cancel{\cancel{(a-5)}}} \cdot \dfrac{\cancel{(a-5)}(a+4)}{(a-3)\cancel{(a+3)}}
\\=\color{blue}{\dfrac{a+4}{a-3}}$
