# How do you evaluate \frac { x } { x ^ { 2} - 9} + \frac { 3} { x ( x - 3) } ?

Nov 20, 2017

$\frac{x}{{x}^{2} - 9} + \frac{3}{x \left(x - 3\right)} = \frac{{x}^{2} + 3 x + 9}{x \left(x - 3\right) \left(x + 3\right)}$

#### Explanation:

$\frac{x}{{x}^{2} - 9} + \frac{3}{x \left(x - 3\right)}$

Factorising the denominator of the first fraction:

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

Putting fractions together by creating a common denominator:

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

Expanding the numerator:

$= \frac{{x}^{2} + 3 x + 9}{x \left(x - 3\right) \left(x + 3\right)}$