Answer
$\dfrac{2(a+4)}{a-3}$
Work Step by Step
The given expression, $
\dfrac{4a+12}{2a-10}\div\dfrac{a^2-9}{a^2-a-20}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4a+12}{2a-10}\cdot\dfrac{a^2-a-20}{a^2-9}
\\\\=
\dfrac{4(a+3)}{2(a-5)}\cdot\dfrac{(a-5)(a+4)}{(a+3)(a-3)}
\\\\=
\dfrac{\cancel{2}(2)(\cancel{a+3})}{\cancel{2}(\cancel{a-5})}\cdot\dfrac{(\cancel{a-5})(a+4)}{(\cancel{a+3})(a-3)}
\\\\=
\dfrac{2(a+4)}{a-3}
.\end{array}
