# How do you solve 4/x-5/3=x/6?

Mar 3, 2018

$\text{x} = 2$
$\text{x} = - 12$

#### Explanation:

What is the least common denominator of 3, x and 6?
6x
1. Multiply everything by 6x to clear out the denominator.
$6 x \left(\frac{4}{x} - \frac{5}{3} = \frac{x}{6}\right)$
$\left(24 - 10 x = {x}^{2}\right)$
2. Looks like a quadratic, solve by factoring
${x}^{2} + 10 x - 24 = 0$
$\left(x - 2\right) \left(x + 12\right) = 0$
$\text{x} = 2$
$\text{x} = - 12$