Answer
$\dfrac{x-4}{x-5}$
Work Step by Step
The given expression, $
\dfrac{x^2+2x-15}{x^2+11x+30}\cdot\dfrac{x^2+2x-24}{x^2-8x+15}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x+5)(x-3)}{(x+5)(x+6)}\cdot\dfrac{(x+6)(x-4)}{(x-3)(x-5)}
\\\\=
\dfrac{(\cancel{x+5})(\cancel{x-3})}{(\cancel{x+5})(\cancel{x+6})}\cdot\dfrac{(\cancel{x+6})(x-4)}{(\cancel{x-3})(x-5)}
\\\\=
\dfrac{x-4}{x-5}
.\end{array}
