# How do you solve the rational equation x / 3 - 2 / 3 = 1 / x?

Jan 28, 2016

$x = - 1 , 3$

#### Explanation:

Notice that the fractions on the left hand side have the same denominator, so they can be combined easily.

$\frac{x - 2}{3} = \frac{1}{x}$

Now, we can cross multiply.

$x \left(x - 2\right) = 3 \left(1\right)$

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

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

This is factorable.

$\left(x - 3\right) \left(x + 1\right) = 0$

This can be split up, since we have two things being multiplied and equalling zero.

$x - 3 = 0 \text{ "" ""or"" "" } x + 1 = 0$

$x = 3 \text{ "" "" "" "" "" } x = - 1$