# How do you subtract 9/(x-2)-5/(x+4)?

Sep 14, 2016

$\frac{9}{x - 2} - \frac{5}{x + 4} = \frac{2 \left(x + 23\right)}{\left(x - 2\right) \left(x + 4\right)}$

#### Explanation:

To subtract fractions you need a common denominator, so let's use $\left(x - 2\right) \left(x + 4\right)$ as our common denominator:

$\frac{9}{x - 2} - \frac{5}{x + 4} = \frac{9 \left(x + 4\right)}{\left(x - 2\right) \left(x + 4\right)} - \frac{5 \left(x - 2\right)}{\left(x - 2\right) \left(x + 4\right)}$

$\textcolor{w h i t e}{\frac{9}{x - 2} - \frac{5}{x + 4}} = \frac{9 \left(x + 4\right) - 5 \left(x - 2\right)}{\left(x - 2\right) \left(x + 4\right)}$

$\textcolor{w h i t e}{\frac{9}{x - 2} - \frac{5}{x + 4}} = \frac{9 x + 36 - 5 x + 10}{\left(x - 2\right) \left(x + 4\right)}$

$\textcolor{w h i t e}{\frac{9}{x - 2} - \frac{5}{x + 4}} = \frac{4 x + 46}{\left(x - 2\right) \left(x + 4\right)}$

$\textcolor{w h i t e}{\frac{9}{x - 2} - \frac{5}{x + 4}} = \frac{2 \left(x + 23\right)}{\left(x - 2\right) \left(x + 4\right)}$