Если 2 модуля равны друг другу, то возможны 2 варианта:
1) (x-1)/(x-2) = -(x+1)/(x+2)
(x-1)/(x-2) + (x+1)/(x+2) = 0
(x-1)(x+2) + (x+1)(x-2) = 0
x^2 + x - 2 + x^2 - x - 2 = 0
2x^2 - 4 = 0
x1 = -√2; x2 = √2
2) (x-1)/(x-2) = (x+1)/(x+2)
(x-1)/(x-2) - (x+1)/(x+2) = 0
(x-1)(x+2) - (x+1)(x-2) = 0
x^2 + x - 2 - x^2 + x + 2 = 0
2x = 0
x3 = 0