How do you solve 5/(y-2)=y+2?

Jan 19, 2016

$y = \pm 3$

Explanation:

$\frac{5}{y - 2} = y + 2$

Multiply both sides times $\left(y - 2\right)$.

$5 = \left(y + 2\right) \left(y - 2\right)$

Expand $\left(y + 2\right) \left(y - 2\right)$.

$5 = {y}^{2} - 4$

Add $4$ to both sides.

$4 + 5 = {y}^{2}$

Simplify.

$9 = {y}^{2}$

Take the square root of both sides.

$\pm \sqrt{9} = \sqrt{{y}^{2}}$

Simplify.

$\pm 3 = y$

Switch sides.

$y = \pm 3$