# How do you add \frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}?

Feb 2, 2017

$\frac{6 \left(y + 14\right)}{\left(y + 4\right) \left(y + 12\right)}$

#### Explanation:

$\frac{12}{{y}^{2} + 16 y + 48} + \frac{6}{y + 4}$
Factorise
$\frac{12}{\left(y + 4\right) \left(y + 12\right)} + \frac{6}{y + 4}$

So to get a common denominator multiply numerator and denominator of the second term by y+12

$= \frac{12}{\left(y + 4\right) \left(y + 12\right)} + \frac{6}{y + 4} \cdot \frac{y + 12}{y + 12}$

$= \frac{12 + 6 \left(y + 12\right)}{\left(y + 4\right) \left(y + 12\right)}$
$= \frac{12 + 6 y + 72}{\left(y + 4\right) \left(y + 12\right)}$
$= \frac{6 y + 84}{\left(y + 4\right) \left(y + 12\right)}$
$= \frac{6 \left(y + 14\right)}{\left(y + 4\right) \left(y + 12\right)}$