# How do you solve 5-3/(2x-1)=(x-4)/(2x-1) and check for extraneous solutions?

Aug 26, 2016

$x = \frac{4}{9}$

#### Explanation:

In $5 - \frac{3}{2 x - 1} = \frac{x - 4}{2 x - 1}$ let us multiply each term by $\left(2 x - 1\right)$, assuming $2 x - 1 \ne 0$ or $x \ne \frac{1}{2}$. We get

$5 \left(2 x - 1\right) - 3 = x - 4$ or

$10 x - 5 - 3 = x - 4$ or

$10 x - x = 5 + 3 - 4$ or

$9 x = 4$ or

$x = \frac{4}{9}$