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

Jan 25, 2018

$x = \frac{25}{11}$

#### Explanation:

Let's add $\frac{1}{x}$ to both sides.

$\frac{4}{5 + x} - \frac{1}{x} = \frac{1}{4 x}$

$\frac{4}{5 + x} = \frac{1}{4 x} + \frac{1}{x}$

We can combine the two fractions on the right pretty easily.

$\frac{4}{5 + x} = \frac{1}{4 x} + \frac{4}{4 x}$

$\frac{4}{5 + x} = \frac{5}{4 x}$

Now that we only have one fraction on each side, we can cross multiply and solve.

$4 \cdot \left(4 x\right) = 5 \cdot \left(5 + x\right)$

$16 x = 25 + 5 x$

$11 x = 25$

$x = \frac{25}{11}$