Решите неравенство: 2/(х+1)-1/(х-1)< 1

Решение внизу на фото

2/x+1-1/x-1<1, x≠-1; x≠1
2/x+1-1/x-1-1<0
2(x-1)-(x+1)*(x-1)/(x+1)*(x-1)<0
2x-2-x-1-(x²-1)/(x+1)*(x-1)<0
2x-2-x-1-x²+1/(x+1)*(x-1)<0
x-2-x²(x+1)*(x-1)<0

{x-2-x²<0
{(x+1)*(x-1)>0

{x-2-x²>0
{(x+1)*(x-1)<0

}x∈R
}x∈[-∞, -1] ∪ [1, +∞]
}x∈∅
x∈[-1, 1

x∈ [-∞, -1) ∪ [ 1, +∞] x≠-1, x≠1