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

Apr 13, 2018

x=3

#### Explanation:

Suggestion, take $\frac{x}{x - 3}$ and throw it to the left side as you can see they have a common denominator. This gives you:
$\frac{3}{x - 3} - \frac{x}{x - 3}$ = $- \frac{3}{2}$
$\frac{3 - x}{x - 3} = - \frac{3}{2}$.
Now, you cross-multiply the right and left sides.
$2 \cdot \left(3 - x\right) = - 3 \cdot \left(x - 3\right)$
$6 - 2 x = - 3 x + 9$ (Just open the brackets)
Now, rearrange terms: $- 2 x + 3 x = 9 - 6$
Which gives x = 3