Answer
$\dfrac{y-5}{y+4}$
Work Step by Step
Adding the numerators and copying the denominator, the given expression, $
\dfrac{y^2-7y}{y^2+8y+16}+\dfrac{6y-20}{y^2+8y+16}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{y^2-7y+6y-20}{y^2+8y+16}
\\\\=
\dfrac{y^2-y-20}{y^2+8y+16}
\\\\=
\dfrac{(y-5)(y+4)}{(y+4)(y+4)}
\\\\=
\dfrac{(y-5)(\cancel{y+4})}{(y+4)(\cancel{y+4})}
\\\\=
\dfrac{y-5}{y+4}
.\end{array}