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

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Answer 1 · 2015-06-04T09:15:00

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

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

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: $color(green)(y = +3 , y = -3$

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