1
3/x-x/(x+1)=(x+4)/x(x+1)
x(x+1)≠0⇒x≠0 U x≠-1
3(x+1)-x*x=x+4
3x+3-x²-x-4=0
x²-2x+1=0
(x-1)²=0
x-1=0
x=1
2
x(3+x)(4-x)≥0
x=0 x=-3 x=4
+ _ + _
-------------[-3]----------[0]-------------[4]--------------------
x∈(-∞;-3] U [0;4]
3
6/(3x-x²)=3x-x²+1
x(3-x)≠0⇒x≠0 U x≠3
(3x-x²)(3x-x²+1)=6
3x-x²=a
a(a+1)=6
a²+a-6=0
a1+a2=-1 U a1*a2=-6
a1=-3⇒3x-x²=-3
x²-3x+3=0
D=9-12=-3<0 нет решения<br>a2=2⇒3x-x²=2
x²-3x+2=0
x1+x2=3 U x1*x2=2⇒x1=1 U x2=2
4
{x²-x-2>0 x1+x2=1 U x18x2=-2⇒x1=-1 U x2=2 ⇒x<-1 U x>2
{-2x²+2x+12>0⇒x²-x-6<0 x1+x2=1 U x1*x2=-6⇒x1=-2 u x2=3 ⇒-2<x<3<br>x∈(-2;-1) U (2;3)