# How do you simplify (6y^3 - 12y^2) /(12y^2 - 18)?

Jul 5, 2015

Factor out the GCF in the numerator and denominator. Cancel the $6$ in the numerator and denominator.

#### Explanation:

$\frac{6 {y}^{3} - 12 {y}^{2}}{12 {y}^{2} - 18}$

Numerator

$6 y 3 - 12 {y}^{2}$

Factor out $6 {y}^{2}$

$6 {y}^{2} \left(y - 2\right)$

Denominator

$\left(12 {y}^{2} - 18\right)$

Factor out $6$.

$6 \left(2 {y}^{2} - 3\right)$

Put them back together.

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

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