#### Answer

$\displaystyle \frac{2y+3}{y-5}$

#### Work Step by Step

To add rational expressions with the same denominator,
add numerators and place the sum over the common denominator.
If possible, factor and simplify the result.
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$\displaystyle \frac{y^{2}+7y}{y^{2}-5y}+\frac{y^{2}-4y}{y^{2}-5y} = \displaystyle \frac{y^{2}+7y+y^{2}-4y}{y^{2}-5y}$
$= \displaystyle \frac{2y^{2}+3y}{y^{2}-5y}$
$= \displaystyle \frac{y(2y+3)}{y(y-5)}\qquad$... reduce the common factor
$=\displaystyle \frac{2y+3}{y-5}$