How do you solve 5 /( y-2) = y+2  and find any extraneous solutions?

Jun 12, 2016

First, let us identify any restrictions on the variable.

Explanation:

In rational equations, restrictions make the denominator be equal to $0$.

Therefore, we can find any restrictions by setting the denominator to 0 and solving.

$y - 2 = 0$

$y = 2$

Thus, $y \ne 2$.

Solving:

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

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

$9 = {y}^{2}$

$\pm 3 = y$

Neither of these contradict the restrictions, therefore our solution set is $\left\{y = \pm 3\right\}$.

Hopefully this helps!