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