Answer
$\dfrac{(x+2)(x-3)}{9}$
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{x^2-4}{9}\cdot\dfrac{x^2-6x+9}{x^2-5x+6}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x+2)(x-2)}{9}\cdot\dfrac{(x-3)(x-3)}{(x-3)(x-2)}
\\\\=
\dfrac{(x+2)(\cancel{x-2})}{9}\cdot\dfrac{(\cancel{x-3})(x-3)}{(\cancel{x-3})(\cancel{x-2})}
\\\\=
\dfrac{(x+2)(x-3)}{9}
.\end{array}
