Answer
$-\dfrac{4(2x+9)}{5}$
Work Step by Step
The given expression, $
\dfrac{4x-12}{2x-9}\div\dfrac{3-x}{4x^2-81}\cdot\dfrac{x+3}{5x+15}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4x-12}{2x-9}\cdot\dfrac{4x^2-81}{3-x}\cdot\dfrac{x+3}{5x+15}
\\\\=
\dfrac{4(x-3)}{2x-9}\cdot\dfrac{(2x+9)(2x-9)}{-(x-3)}\cdot\dfrac{x+3}{5(x+3)}
\\\\=
\dfrac{4(\cancel{x-3})}{\cancel{2x-9}}\cdot\dfrac{(2x+9)(\cancel{2x-9})}{-(\cancel{x-3})}\cdot\dfrac{\cancel{x+3}}{5(\cancel{x+3})}
\\\\=
\dfrac{4(2x+9)}{-5}
\\\\=
-\dfrac{4(2x+9)}{5}
.\end{array}
