(x+1)(x²-x+1)/(x+1)+3/(x²-x+1)≤4
(x²-x+1)+3/(x²-x+1)≤4,x≠-1
x²-x+1=a
a+3/a-4≤0
(a²-4a+3)/a≤0
a²-4a+3=0
a1+a2=4 U a1*a2=3
a1=1 U a2=3
a=0
_ + _ +
---------------(0)----------------[1]----------------[3]------------------
a<0⇒x²-x+1<0<br>D=1-4=-3 решения нет
1≤a≤3
1)x²-x+1≥1
x²-x≥0
x(x-1)≥0
x=0 U x=1
x≤0 U x≥1
2)x²-x+1≤3
x²-x-2≤0
x1+x2=1 U x1*x2=-2
x1=-1 U x2=2 U x≠-1
-1x∈(-1;0] U [1;2]