Answer
$\dfrac{y-9}{(y+1)(y-1)}$
Work Step by Step
Using the $LCD=
(y+1)(y-1)
$, the given rational expression, $
\dfrac{5}{y+1}-\dfrac{4}{y-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(y-1)(5)-(y+1)(4)}{(y+1)(y-1)}
\\\\=
\dfrac{5y-5-4y-4}{(y+1)(y-1)}
\\\\=
\dfrac{y-9}{(y+1)(y-1)}
.\end{array}
