X/(x + 1) - 1/(x - 1) - 2/(x² - 1) = 0
x/(x + 1) - 1/(x - 1) - 2/(x - 1)(x + 1) = 0
ОДЗ:
x ≠ -1; 1
Умножим всё уравнение на (x - 1)(x + 1).
x(x - 1) - (x + 1) - 2 = 0
x² - x - x - 1 - 2 = 0
x² - 2x - 3 = 0
x² - 2x + 1 - 4 = 0
(x - 1)² - 2² = 0
(x - 1 - 2)(x - 1 + 2) = 0
(x - 3)(x + 1) = 0
x = -1 - не уд. ОДЗ; x = 3.
Ответ: x = 3.