Answer
$\dfrac{2}{y-5}$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{2y^2+2}{y^3-5y^2+y-5}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2(y^2+1)}{(y^3-5y^2)+(y-5)}
\\\\=
\dfrac{2(y^2+1)}{y^2(y-5)+(y-5)}
\\\\=
\dfrac{2(y^2+1)}{(y-5)(y^2+1)}
\\\\=
\dfrac{2(\cancel{y^2+1})}{(y-5)(\cancel{y^2+1})}
\\\\=
\dfrac{2}{y-5}
.\end{array}
