Answer
$\dfrac{5k^2-7k+4}{(k+2)(k-2)(k-1)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{5k}{k^2-4}-\dfrac{2}{k^2+k-2}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{5k}{(k+2)(k-2)}-\dfrac{2}{(k+2)(k-1)}
.\end{array}
Using the $LCD=
(k+2)(k-2)(k-1)
,$ then the given expression simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(k-1)(5k)-(k-2)(2)}{(k+2)(k-2)(k-1)}
\\\\=
\dfrac{5k^2-5k-2k+4}{(k+2)(k-2)(k-1)}
\\\\=
\dfrac{5k^2-7k+4}{(k+2)(k-2)(k-1)}
.\end{array}
