# How do you combine x / (x^2-4) + (3x - 5) /(x^2 + 4x + 4)?

##### 1 Answer
May 26, 2015

In order to create a common denominator note that
$\left({x}^{2} - 4\right) \left(x + 2\right) = \left(x - 2\right) \left(x + 2\right) \left(x + 2\right) = \left(x - 2\right) \left({x}^{2} + 4 x + 4\right)$

So
$\frac{x}{{x}^{2} - 4} + \frac{3 x - 5}{{x}^{2} + 4 x + 4}$

$= \frac{x \left(x + 2\right) + \left(3 x - 5\right) \left(x - 2\right)}{\left(x - 2\right) \left(x + 2\right) \left(x + 2\right)}$

$= \frac{{x}^{2} + 2 x + 3 {x}^{2} - 11 x + 15}{\left(x - 2\right) \left(x + 2\right) \left(x + 2\right)}$

$= \frac{4 {x}^{2} - 9 x + 15}{{x}^{3} + 2 {x}^{2} - 4 x - 8}$