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

Apr 4, 2018

$y = \pm 3$

#### Explanation:

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

First of all, we multiply both sides by $y - 2$:
$5 = \left(y + 2\right) \left(y - 2\right)$

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

$9 = {y}^{2}$

$y = \pm 3$

Now we have to check both of our solutions back into the original equation to make sure both are really solutions:
$\frac{5}{- 3 - 2} = - 3 + 2$

$\frac{5}{-} 5 = - 1$

$- 1 = - 1$

Now we know that $- 3$ works. Now let's check $3$:
$\frac{5}{3 - 2} = 3 + 2$

$\frac{5}{1} = 5$

$5 = 5$

Good. Both solutions work. So the answer is $y = \pm 3$.

Hope this helps!

Apr 4, 2018

$y = \pm 3$

#### Explanation:

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

Multiply $\left(y - 2\right)$ on both the sides

5/cancel((y - 2)) × cancel((y -2)) = (y + 2) × (y -2)

5 = (y + 2) × (y - 2)

5 = y^2 - 2^2 color(white)(..)[∵ (a + b)(a - b) = a^2 - b^2)

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

Add $4$ on both the sides

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

$9 = {y}^{2}$

Square root on both the sides

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

$\textcolor{b l u e}{y = \pm 3}$