Posted by Amy on Wednesday, January 19, 2011 at 1:20pm.
(4/(x + 2) - 4/x)/2 = 1
rewrite as
(4/(x + 2) - 4/x) * 1/2 = 1
4/(2(x + 2)) - 4/2x = 1
4/(2x + 4) - 4/2x = 1
LCD 2x(2x + 4)
(8x - 4(2x + 4))/(2x(2x + 4)) = 1
multiply both sides by 2x(2x + 4)
8x - 4(2x + 4) = 2x(2x + 4)
8x - 8x -16 = 4x^2 + 8x
-16 = 4x^2 + 8x
4x^2 + 8x + 16 = 0
4(x^2 + 2x + 4) = 0
divide both sides by 4
x^2 + 2x + 4 = 0
Solve this by Quadratic formula or completing the square
I leave the rest to you to solve