1
1/(x-1)+1/(2-x)-5≤0
(2-x+x-1-15x+5x²+10)/(1-x)(2-x)≤0
(5x²-15x+11)/(x-1)(2-x)≤0
5x²-15x+11=0
D=225-220=5
x1=(15-√5)/10 U x2=(15+√5)/10
x-1=0⇒x=1 U 2-x=0⇒x=2
_ + _ + _
-----------(1)-----------[(15-√5)/10]---------[(15+√5)/10]----------(2)----------------
x∈(-∞;1) U [(15-√5)/10;(15+√5)/10] U (2;∞)
2
(2-1/(x-6):(5/(x-6)-1)+1/5≤0
(2x-12-1)/(x-6) :(5-x+6)/(x-6)-1/5≤0
(2x-13)/(x-6)*(x-6)/(11-x)-1/5≤0
(2x-13)/(11-x)-1/5≤0,x≠6
(10x-65-11+x)/5(11-x)≤0
(11x-76)/5(11-x)≤0
x=76/11 x=11
_ + _
-------------[76/11]-----(11)----------------
x∈(-∞;6) U (6;76/11] U (11;∞)
3
5x-11=a,x≠2,2
(10/a+a/10)²-(5/2)²≤0
(10/a+a/10-5/2)(10/a+a/10+5/2)≤0
(100+a²-25a)(100+a²+25)/100a²≤0
a²-25a+100=0
a1+a2=25 U a1*a2=100⇒a1=5 U a2=20
a²+25a+100=0
a1+a2=-25 U a1*a2=100⇒a1=-5 U a2=-20
+ _ + + _ +
--------------[-20]---------[-5]--------(0)-------[5]-----------[20]------------------
-20≤a≤-5⇒-20≤5x-21≤-5⇒1≤5x≤6⇒0,2≤x≤3,2
5≤a≤20⇒5≤5x-21≤20⇒26≤5x≤41⇒5,2≤x≤8,2
x∈[0,2;3,2] U [5,2;8,2]