# How do you solve the rational equation 5/(y-2) = y+2?

Jul 17, 2018

$y = \pm 3$

#### Explanation:

$\text{multiply both sides by } y - 2$

$\cancel{y - 2} \times \frac{5}{\cancel{y - 2}} = \left(y + 2\right) \left(y - 2\right)$

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

$\text{add 4 to both sides}$

$9 = {y}^{2}$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\pm \sqrt{9} = y \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow y = \pm 3$

Jul 17, 2018

$y = \pm 3$

#### Explanation:

First of all it must be $y \ne 2$, and we can multiply the whole equation by $y - 2$ and we get

$5 = \left(y - 2\right) \left(y + 2\right)$ now we use that

$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

so we get

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

adding $4$

$9 = {y}^{2}$

so we get $y = \pm 3$