First, we each side of the equation by a common denominator (in this case 8(x - 2)) to eliminate the fraction and keep the equation balanced:
8(x - 2) (x + 2)/(x - 2) = 8(x - 2) 4/8
8cancel((x - 2)) (x + 2)/cancel((x - 2)) = cancel(8)(x - 2) 4/cancel(8)
8(x + 2) = 4(x - 2)
Now we can expand the terms in parenthesis on each side of the equation:
8x + 16 = 4x - 8
Next we can isolate the x terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:
8x + 16 - 16 - 4x = 4x - 8 - 16 - 4x
8x + 0 - 4x = 0 - 24
8x - 4x = -24
4x = -24
Finally, we can solve for x while keeping the equation balanced:
(4x)/4 = (-24)/4
(cancel(4)x)/cancel(4) = -6
x = -6
