(x - 2)/(x + 2) = x - 3
(x + 2)(x - 2)/(x + 2) = (x + 2)(x - 3)
x - 2 = x^2 - x - 6
0 = x^2 - 2x - 4
0 = x^2 - 2x + 1 - 5
0 = (x - 1)^2 - 5
5 = (x - 1)^2
x - 1 = √5 or x - 1 = -√5
x = 1 + √5 or x = 1 - √5
(x + 2)(x - 2)/(x + 2) = (x + 2)(x - 3)
x - 2 = x^2 - x - 6
0 = x^2 - 2x - 4
0 = x^2 - 2x + 1 - 5
0 = (x - 1)^2 - 5
5 = (x - 1)^2
x - 1 = √5 or x - 1 = -√5
x = 1 + √5 or x = 1 - √5
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multiply both sides by (x+2) that should help ;)