# How do you solve x/ (x-3) - 3/2 = 3/ (x-3) and find any extraneous solutions?

Jun 4, 2017

No real solutions.

One extraneous solution: $x = 3$

#### Explanation:

Multiply both sides by $x - 3$:

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

$x - \frac{3}{2} x + \frac{9}{2} = 3$

$- \frac{1}{2} x = - \frac{3}{2}$

$x = 3$

Now to check if $x = 3$ is extraneous, plug it back into the original problem:

3/(3-3) - 3/2 stackrel(?)(=) 3/(3-3)

3/0 - 3/2 stackrel(?)(=) 3/0

Hmm... we can't divide by 0, so this solution doesn't work. Therefore, $x = 3$ is an extraneous solution.