# How do you simplify (6y^2 + 18y)/( 2y^3 - 6y^2 - 36y )?

Oct 7, 2015

$\frac{3}{y - 6}$

#### Explanation:

$\frac{6 {y}^{2} + 18 y}{2 {y}^{3} - 6 {y}^{2} - 36 y}$

$\frac{6 \cancel{y} \left(y + 3\right)}{2 \cancel{y} \cdot \left({y}^{2} - 3 y - 18\right)} = \frac{3 \left(y + 3\right)}{{y}^{2} - 3 y - 18}$

You can write the denominator as

${y}^{2} - 3 y - 18 = {y}^{2} - 6 y + 3 y - 18$

$y \cdot \left(y + 3\right) - 6 \left(y + 3\right) = \left(y + 3\right) \cdot \left(y - 6\right)$

The expression will thus be

$\frac{3 \cdot \cancel{y + 3}}{\cancel{y + 3} \cdot \left(y - 6\right)} = \frac{3}{y - 6}$