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

Jun 4, 2015

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

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

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

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

 color(blue)(y^2 +4y - 5 = 0

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

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

$y \left(y + 5\right) - 1 \left(y + 5\right) = 0$

color(blue)((y-1)(y+5) = 0

the solutions for the expression are: color(blue)(y = 1 , y = -5