# How do you solve 1/2(x-3)+3/(2-x)=5 x?

Mar 1, 2016

First, distribute.

#### Explanation:

$\frac{x - 3}{2} + \frac{3}{2 - x} = 5 x$

The LCD (least common denominator) is $\left(2\right) \left(2 - x\right)$

$\frac{\left(x - 3\right) \left(2 - x\right)}{\left(2\right) \left(2 - x\right)} + \frac{\left(3\right) \left(2\right)}{\left(2 - x\right) \left(2\right)} = \frac{\left(5 x\right) \left(2\right) \left(2 - x\right)}{\left(2\right) \left(2 - x\right)}$

You can now eliminate the denominators since everything is equivalent,

$- {x}^{2} - 3 x + 2 x - 6 + 6 = 20 x - 10 {x}^{2}$

$- {x}^{2} - 21 x + 10 {x}^{2} = 0$

$9 {x}^{2} - 21 x = 0$

$3 x \left(3 x - 7\right) = 0$

$x = 0 \mathmr{and} \frac{7}{3}$

Hopefully this helps!