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

Apr 27, 2018

$y = \pm 3$

#### Explanation:

By transposing the terms and using simple algebra, we get-

5=(y+2)(y-2)
Using ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$,
5= ${y}^{2} - 4$
${y}^{2} = 9$
$y = \pm 3$

Apr 27, 2018

$y = \pm 3$

#### Explanation:

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

Multiply both sides by $y - 2$:
$\frac{5}{\cancel{\left(y - 2\right)}} \cancel{\textcolor{red}{\cdot \left(y - 2\right)}} = \left(y + 2\right) \textcolor{red}{\left(y - 2\right)}$

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

Add $4$ on both sides of the equation:

$5 \quad \textcolor{red}{+ \quad 4} = {y}^{2} - 4 \quad \textcolor{red}{+ \quad 4}$

$9 = {y}^{2}$

Therefore, $y = \pm 3$

($\pm$ refers to "plus or minus")

Hope this helps!