# How do you solve \frac { x + 5} { 2x ^ { 2} } + \frac { 1} { 4x ^ { 2} } = \frac { 4x + 8} { x ^ { 2} }?

Apr 10, 2018

You'll want to remove the denominators first.

#### Explanation:

This means you multiply the left and right hand sides of the equation by $4 {x}^{2}$.

$\frac{x + 5}{2 {x}^{2}} + \frac{1}{4 {x}^{2}} = \frac{4 x + 8}{x} ^ 2$

$2 \left(x + 5\right) + 1 = 4 \left(4 x + 8\right)$

Then you expand and move the $x$s to one side and the integers to the other.

$2 x + 10 + 1 = 16 x + 32$

$10 + 1 - 32 = 16 x - 2 x$

$- 21 = 14 x$

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