# How do you simplify \frac { - 3y ^ { 2} + 27} { y ^ { 2} + 7y + 12}?

Nov 20, 2017

$\frac{- 3 \left(y - 3\right)}{y + 4}$

#### Explanation:

Numerator:

$- 3 \left({y}^{2} - 9\right)$

$- 3 \left(y - 3\right) \left(y + 3\right)$

Denominator:
factor ${y}^{2} + 7 y + 12$

$= \left(y + 3\right) \left(y + 4\right)$

Together:

$\frac{- 3 \left(y - 3\right) \left(y + 3\right)}{\left(y + 3\right) \left(y + 4\right)}$

$= \frac{- 3 \left(y - 3\right)}{y + 4}$

That $\left(y + 3\right)$canceled each other. The result would be the answer