Answer
$\dfrac{4}{(x+2)(x+3)}$
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{x^2-6x+9}{x^2-x-6}\div\dfrac{x^2-9}{4}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2-6x+9}{x^2-x-6}\cdot\dfrac{4}{x^2-9}
\\\\=
\dfrac{(x-3)(x-3)}{(x-3)(x+2)}\cdot\dfrac{4}{(x+3)(x-3)}
\\\\=
\dfrac{(\cancel{x-3})(\cancel{x-3})}{(\cancel{x-3})(x+2)}\cdot\dfrac{4}{(x+3)(\cancel{x-3})}
\\\\=
\dfrac{4}{(x+2)(x+3)}
.\end{array}
