Answer
$\dfrac{4(a-3)}{(a-9)(a-9)}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $
\dfrac{a^2-a-6}{a^2-81}\div\dfrac{a^2-7a-18}{4a+36}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a^2-a-6}{a^2-81}\cdot\dfrac{4a+36}{a^2-7a-18}
\\\\=
\dfrac{(a-3)(a+2)}{(a+9)(a-9)}\cdot\dfrac{4(a+9)}{(a-9)(a+2)}
\\\\=
\dfrac{(a-3)(\cancel{a+2})}{(\cancel{a+9})(a-9)}\cdot\dfrac{4(\cancel{a+9})}{(a-9)(\cancel{a+2})}
\\\\=
\dfrac{4(a-3)}{(a-9)(a-9)}
.\end{array}
