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

Jun 19, 2016

$x = 3$ or $x = - 1$

#### Explanation:

Given:

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

Multiply both sides by $3 x$ to get:

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

Expand the left hand side and subtract $3$ from both sides to get:

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

Factoring the left hand side we find:

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

So:

$x = 3$ or $x = - 1$

You can check these values by substituting back into the original equation:

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

$\frac{\left(- 1\right) - 2}{3} = - \frac{3}{3} = - 1 = \frac{1}{- 1}$