F.4math help !!!

since g(x) = 2x / (1-x)
we have
g(2x) = 2(2x) / (1 - 2x) and 1 - g(x) = (1 - x - 2x) / (1 - x) = (1 - 3x) / (1 - x)

g(2x) / (1 - g(x)) = -2/3
4x / (1- 2x) = (-2/3) (1 - 3x) / (1 - x)
4x(3)(1 - x) = (-2) (1 - 3x) (1 - 2x)
12x - 12x^2 = (-2) (1 - 5x + 6x^2)
= -2 + 10x - 12x^2
12x = -2 + 10x
2x = -2
x = -1

g(2x)/1-g(x) = -2/3
g(2x) = 2{2x/(1-x)} = 4x/1-x
1-g(x) = 1 - (2x/1-x) = (1-x/1-x) - (2x/1-x) = (1-x-2x)/(1-x) = 1-3x/1-x
g(2x)/1-g(x) = -2/3
(4x/1-x)/(1-3x/1-x) = -2/3
(4x/1-x) * (1-x/1-3x) = -2/3
4x/1-3x = -2/3
3(4x) = -2(1-3x)
12x = -2+6x
6x = -2
x = -1/3