Перепишем: 2/(1-x^2) - 1/(1-x) + 4/(x+1)^2 = 0.
2/((1-x)(1+x)) - (1+x)/(1-x)(1+x) + 4/(x+1)^2 = 0.
2/(1-x^2) - (1+x)/(1-x^2) + 4/(x+1)^2 = 0.
(2 - (1+x)) / (1-x^2) + 4/(x+1)^2 = 0.
(1-x) / ((1-x)(1+x)) + 4/(x+1)^2 = 0.
1/(1+x) + 4/(x+1)^2 = 0.
Общий знаменатель (x+1)^2.
(x+1) + 4 = 0.
x + 5 = 0.
x = -5.
Ответ: -5