Answer
$\dfrac{x+3}{-2(x+2)}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{5x-15}{3-x}\cdot \dfrac{x+2}{10x+20}\cdot \dfrac{x^2-9}{x^2-x-6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5(x-3)}{-(x-3)}\cdot \dfrac{x+2}{10(x+2)}\cdot \dfrac{(x+3)(x-3)}{(x-3)(x+2)}
\\\\=
\dfrac{\cancel{5}(\cancel{x-3})}{-(\cancel{x-3})}\cdot \dfrac{\cancel{x+2}}{\cancel{5}\cdot2(\cancel{x+2})}\cdot \dfrac{(x+3)(\cancel{x-3})}{(\cancel{x-3})(x+2)}
\\\\=
\dfrac{x+3}{-2(x+2)}
.\end{array}
