# How do you combine (y-2)/(y-4)+(2y^2-15y+12)/(y^2-16)?

Jul 21, 2016

$\frac{3 y - 1}{y + 4}$.

#### Explanation:

The Expression$= \frac{y - 2}{y - 4} + \frac{2 {y}^{2} - 15 y + 12}{\left(y - 4\right) \left(y + 4\right)}$

The $L . C . M .$ of the $D r s .$ is ${y}^{2} - 16 = \left(y - 4\right) \left(y + 4\right)$

$\therefore t h e E x p . = \frac{\left(y - 2\right) \left(y + 4\right) + 2 {y}^{2} - 15 y + 12}{\left(y - 4\right) \left(y + 4\right)}$

$= \frac{\left({y}^{2} + 2 y - 8 + 2 {y}^{2} - 15 y + 12\right)}{\left(y - 4\right) \left(y + 4\right)}$

$= \frac{3 {y}^{2} - 13 y + 4}{\left(y - 4\right) \left(y + 4\right)}$

$= \frac{\cancel{\left(y - 4\right)} \left(3 y - 1\right)}{\cancel{\left(y - 4\right)} \left(y + 4\right)}$

$= \frac{3 y - 1}{y + 4}$.