# How do you solve 3/(x-3)=x/(x-3)-3/2?

Mar 3, 2018

No solutions for $x$

#### Explanation:

First subtract $\frac{3}{x - 3}$ from both sides:

$0 = \frac{x}{x - 3} - \frac{3}{x - 3} - \frac{3}{2}$

Simplifying:

$0 = \frac{x - 3}{x - 3} - \frac{3}{2}$

We can cancel, the $\left(x - 3\right)$ as it is on both bottom and top

$0 = \frac{\cancel{\left(x - 3\right)}}{\cancel{\left(x - 3\right)}} - \frac{3}{2}$

$\implies 0 = 1 - \frac{3}{2}$

$\implies 0 = - \frac{1}{2}$

But we know this is not true, so hence there are no solutions to this problem!