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

May 31, 2017

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

#### Explanation:

First rearrange the equation so that it looks like this:

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

Make the right hand side of the equation have a denominator of 6.

$\frac{2}{3 x} = \frac{3 x}{6} - \frac{4}{6}$

= $\frac{2}{3 x} = \frac{3 x - 4}{6}$

Now cross multiply to have a linear equation:

$3 x \left(3 x - 4\right) = 12$

$9 {x}^{2} - 12 x - 12 = 0$

The equation is divisible by 3 to give this equation:

$3 {x}^{2} - 4 x - 4 = 0$

Now factorise the equation:

$\left(3 x + 2\right) \left(x - 2\right) = 0$

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