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

Jun 4, 2015

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

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

We know the Difference of Squares Identity which says:
color(blue) ((a+b)(a-b) = (a^2 - b^2)

color(blue)((y+2)(y-2) = y^2 - 2^2 = y^2-4

the expression now becomes:

$5 = {y}^{2} - 4$
$9 = {y}^{2}$
 y = sqrt9 = color(green)( +3 or -3

the solutions for the expression are:  color(green)(y = +3 , y = -3