# How do you simplify 4/(x+3) –6/(x-3)?

Feb 4, 2015

The answer is: $- 2 \frac{x + 15}{\left(x + 3\right) \left(x - 3\right)}$.

The least common denominator of the two denominators $x + 3$ and $x - 3$ is:

$\left(x + 3\right) \left(x - 3\right)$,

so:

$\frac{4}{x + 3} - \frac{6}{x - 3} = \frac{4 \left(x - 3\right) - 6 \left(x + 3\right)}{\left(x + 3\right) \left(x - 3\right)} =$

$= \frac{4 x - 12 - 6 x - 18}{\left(x + 3\right) \left(x - 3\right)} = \frac{- 2 x - 30}{\left(x + 3\right) \left(x - 3\right)} =$

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