# How do you solve x/5 - 4/5 = 1/x ?

Dec 15, 2015

$x = 5$ and $x = - 1$

#### Explanation:

Original Equation:
$\frac{x}{5} - \frac{4}{5} = \frac{1}{x}$

First, subtract the two fractions on the left:
$\frac{x - 4}{5} = \frac{1}{x}$

Next, cross multiply:
$x \left(x - 4\right) = 5$

Multiply the left out:
${x}^{2} - 4 x = 5$

Bring the $5$ over:
${x}^{2} - 4 x - 5 = 0$

Factor:
$\left(x - 5\right) \left(x + 1\right) = 0$

Solve:
$x = 5$ and $x = - 1$