Answer
$\dfrac{3}{8r}$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{3r^3-9r^2}{r^2-9}\div\dfrac{8r^3}{r+3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3r^3-9r^2}{r^2-9}\cdot\dfrac{r+3}{8r^3}
\\\\=
\dfrac{3r^2(r-3)}{(r+3)(r-3)}\cdot\dfrac{r+3}{8r^3}
\\\\=
\dfrac{3\cancel{r^2}(\cancel{r-3})}{(\cancel{r+3})(\cancel{r-3})}\cdot\dfrac{\cancel{r+3}}{8\cancel{r^2}(r)}
\\\\=
\dfrac{3}{8r}
.\end{array}
