(x²-|2x-3|)/(x²-|2-x|)≤1
1)x<1,5<br>(x²+2x-3)/(x²-2+x)-1≤0
(x²+2x-3-x²+2-x)/(x²+x-2)≤0
x²+x-2=0
x1+x2=-1 U x1*x2=-2⇒x1=-2 U x2=1
(x-3)/(x-1)(x+2)≤0
x=3 x=1 x=-2
_ + _ +
--------------(-2)--------(1)-------------[3]---------------
x<-2 U 1<x<1,5<br>2)1,5≤x≤2
(x²-2x+3)/(x²-2+x)-1≤0
(x²-2x+3-x²+2-x)/(x²+x-2)≤0
(-3x+5)/(x-1)(x+2)≤0
x=1 2/3 x=1 x=-2
+ _ + _
-----------(-2)-------------(1)-------------[1 2/3]--------------
1 2/3≤x≤2
3)x>2
(x²-2x+3)/(x²+2-x)-1≤0
(x²-2x+3-x²-2+x)/(x²-x+2)≤0
(1-x)/(x²-x+2)≤0
x²-x+2=0
D=1-8=-7<0⇒при любом х x²-x+2>0⇒
1-x≤0⇒x≥1
x>2
Ответ x∈(-∞;-2) U (1;1,5) U [1 2/3;∞)