Answer
$\dfrac{p(p+8)}{(2p+1)(p-5)(3p-2)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{p}{2p^2-9p-5}-\dfrac{2p}{6p^2-p-2}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{p}{(2p+1)(p-5)}-\dfrac{2p}{(2p+1)(3p-2)}
.\end{array}
Using the $LCD=
(2p+1)(p-5)(3p-2)
,$ the expression, $
\dfrac{p}{(2p+1)(p-5)}-\dfrac{2p}{(2p+1)(3p-2)}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(3p-2)(p)-(p-5)(2p)}{(2p+1)(p-5)(3p-2)}
\\\\=
\dfrac{3p^2-2p-2p^2+10p}{(2p+1)(p-5)(3p-2)}
\\\\=
\dfrac{p^2+8p}{(2p+1)(p-5)(3p-2)}
\\\\=
\dfrac{p(p+8)}{(2p+1)(p-5)(3p-2)}
.\end{array}
