How do you solve $\frac{5}{y - 2} = y + 2$ $5/(y-2)=y+2$ ?

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Answer 1 · 2016-01-19T02:42:02

$y = \pm 3$ $y=+-3$

$\frac{5}{y - 2} = y + 2$ $5/(y-2)=y+2$

Multiply both sides times $(y - 2)$ $(y-2)$ .

$5 = (y + 2) (y - 2)$ $5=(y+2)(y-2)$

Expand $(y + 2) (y - 2)$ $(y+2)(y-2)$ .

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

Add $4$ $4$ to both sides.

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

Simplify.

$9 = y^{2}$ $9=y^2$

Take the square root of both sides.

$\pm \sqrt{9} = \sqrt{y^{2}}$ $+-sqrt 9=sqrt (y^2)$

Simplify.

$\pm 3 = y$ $+-3=y$

Switch sides.

$y = \pm 3$ $y=+-3$

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