How do you solve (x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)?

1 Answer
Xytl
Jan 24, 2017

x-4 = ((x-2)(x-2))/(x+2) + 1
(x-4)(x+2) = (x-2)(x-2) + (x+2)
x^2 - 2x - 8 = x^2-4x+4 + x + 2

Simplify
2x - 12 = x + 2
x = 14

Explanation:

The easiest way to do this type of calculation is to get rid of all the denominators. To do this, first times every single term by x-2, then do the same, but with x+2. At that point, it becomes a matter of simplification.

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