Correct answer: x in (-inf, -2) U (-2, -1) U (1, inf)
The factor (x+2)² is non-negative and equals zero only at x = -2 (excluded since we need strict <0, but at x=-2 the expression is 0, not <0, so x=-2 is excluded). Rewriting: ((x-1)(x+2)²)/(-(x+1)) < 0 is equivalent to ((x-1)(x+2)²)/(x+1) > 0. Sign analysis of (x-1)/(x+1) (with (x+2)² > 0 for x != -2) gives the solution x < -1 or x > 1, excluding x = -2 where the expression is zero. So x in (-inf,-2) U (-2,-1) U (1, inf).