1)(x+1)/(x-2)>3
(x+1-3x+6)/(x-2)>0
(7-2x)/(x-2)>0
x=3,5 x=2
- + -
_________________________
2 3,5
x∈(2;3,5)
2)(x-1)/(x-3)<3<br>(x-1-3x+9)/(x-3)<0<br>(8-2x)/(x-3)<0<br>x=4 x=3
_ + _
____________________________
3 4
x∈(-∞;3) U (4;∞)
3)(x-1)/(x-3)>3
(x-1-3x+9)/(x-3)>0
(8-2x)/(x-3)>0
x=4 x=3
_ + _
____________________________
3 4
x∈(3;4)
4)(x-1)/(x+3)<(x+3)/(x-1)<br>(x²-2x+1-x²-6x-9)/(x-1)(x+3)<0<br>(-8x-8)/(x-1)(x+3)<0<br>8(x+1)/(x-1)(x+3)>0
x=-1 x=1 x=-3
_ + _ +
____________________________________
-3 -1 1
x∈(-3;-1) U (1;∞)
5)(x-2)/(x+4)>(x+4)/(x-2)
(x²-4x+4-x²-8x-16)/(x-2)(x+4)>0
-12(x+1)/(x-2)(x+4)>0
x=-1 x=2 x=-4
+ _ + _
______________________________
-4 -1 2
x∈(-∞;-4) U (-1;2)
6)x/(x-1)>0
x=0 x=1
+ _ +
_______________________________
0 1
x∈(-∞;0) U (1;∞)