4/(x+1)≥(4/(3x-3)+5/(3x+6)
ОДЗ: x+1≠0 x≠-1 x-1≠0 x≠1 x+2≠0 x≠-2
4/(x+1)≥4/(3*(x-1))+5/(3*(x+2)) |×3
4*3/(x+1)≥4/(x-1)+5/(x+2)
12/(x+1)-4/(x-1)-5/(x+2)≥0
(12*(x-1)*(x+2)-4*(x+1)*(x+2)-5*(x+1)*(x-1))/((x+1)*(x-1)*(x+2))≥0
(12x²+12x-24-4x²-12x-8-5x²+5)/((x+1)*(x-1)*(x+2)x+1))≥0
(3x²-27)/((x+1)*(x-1)*(x+2))≥0
3*(x²-9)/((x+1)*(x-1)*(x+2)≥0 |÷3
(x+3)*(x-3)/((x+1)*(x-1)*(x+2))≥0
-∞__-__-3__+__-2__-__-1__+__1__-__3__+__+∞
x∈[-3;-2)U(-1;1)U[3;+∞). ⇒
Ответ: x=-3.