# How do you simplify \frac { 4y } { y ^ { 2} - 9} - \frac { 12} { y ^ { 2} - 9}?

Apr 22, 2018

$\implies \frac{4}{y + 3}$

#### Explanation:

The denominator is the same...

$\implies \frac{4 y - 12}{{y}^{2} - 9}$

Factor $4 y - 12 \to 4 \left(y - 3\right)$

Use difference in two squares : ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

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

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

Cancel:

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

$\implies \frac{4}{y + 3}$