# How do you combine 3/(x-3) - 1/x ?

Jan 2, 2016

Place on a common denominator for an answer of $\frac{2 x + 3}{{x}^{2} - 3 x}$

#### Explanation:

$\frac{3}{x - 3} - \frac{1}{x}$

The common denominator of these fractions is $x \left(x - 3\right) = {x}^{2} - 3 x$.

$= \frac{3}{x - 3} \left(\frac{x}{x}\right) - \frac{1}{x} \left(\frac{x - 3}{x - 3}\right)$

$= \frac{3 x}{{x}^{2} - 3 x} - \frac{x - 3}{{x}^{2} - 3 x}$

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

Don't forget to distribute the negative.

$= \frac{2 x + 3}{{x}^{2} - 3 x}$