# How do you solve  3/(x-3) + 4/x +1/3 = x/(x-3) and find any extraneous solutions?

Jun 1, 2018

$x = 6$

#### Explanation:

$\frac{3}{x - 3} + \frac{4}{x} + \frac{1}{3} = \frac{x}{x - 3}$

$\frac{4}{x} + \frac{1}{3} = \frac{x - 3}{x - 3}$

I assumed $x \ne 3$, because $x = 3$ is extraneous solution. Hence,

$\frac{4}{x} + \frac{1}{3} = 1$

$\frac{4}{x} = \frac{2}{3}$

$x = 3 \cdot \frac{4}{2} = 6$