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

Oct 3, 2016

$y = - 1 \text{ or } y = - 5$

Explanation:

$\frac{5}{y} - 2 = y + 2 \text{ } \leftarrow$ move the -2 to the RHS

$\frac{5}{y} = y + 4 \text{ } \leftarrow \times y$ to get rid of the fractions.

$5 = {y}^{2} + 4 y \text{ } \leftarrow$ make = 0.

${y}^{2} + 4 y - 5 = 0$

$\left(y - 1\right) \left(y + 5\right) = 0 \text{ } \leftarrow$ solve for y.

$y - 1 = 0 \rightarrow y = 1$

$y + 5 = 0 \rightarrow y = - 5$