Answer
$y-7$
Work Step by Step
When subtracting two fractions with common denominators, we subtract the numerators and copy the denominator. Therefore, the given expression, $
\dfrac{y^2}{y+2}-\dfrac{5y+14}{y+2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{y^2-(5y+14)}{y+2}
\\\\=
\dfrac{y^2-5y-14}{y+2}
\\\\=
\dfrac{(y-7)(y+2)}{y+2}
\\\\=
\dfrac{(y-7)(\cancel{y+2})}{\cancel{y+2}2}
\\\\=
y-7
.\end{array}