Answer
$1$
Work Step by Step
The given expression, $
\dfrac{p^2-p-12}{p^2-2p-15}\cdot\dfrac{p^2-9p+20}{p^2-8p+16}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(p-4)(p+3)}{(p-5)(p+3)}\cdot\dfrac{(p-4)(p-5)}{(p-4)(p-4)}
\\\\=
\dfrac{(\cancel{p-4})(\cancel{p+3})}{(\cancel{p-5})(\cancel{p+3})}\cdot\dfrac{(\cancel{p-4})(\cancel{p-5})}{(\cancel{p-4})(\cancel{p-4})}
\\\\=
1
.\end{array}
