# How do you solve 5x-\frac{1}{x}=4?

May 21, 2018

$x = - \frac{1}{5} \mathmr{and} x = 1$

#### Explanation:

Multiply everything by $x$ to remove the fraction.

$5 x - \frac{1}{x} = 4$ $\implies 5 {x}^{2} - 1 = 4 x$

$5 {x}^{2} - 4 x - 1 = 0$

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

$5 x + 1 = 0 \mathmr{and} x - 1 = 0$

$x = - \frac{1}{5} \mathmr{and} x = 1$