1
(x-1)/(2x-5)>0
x=1 x=2,5
+ _ +
----------------(1)---------------(2,5)------------------
x∈(-∞;1) U (2,5;∞)
2
(x-1)(x+1)/(x+3)(5-2x)≤0
x=1 x=-1 x=-3 x=2,5
_ + _ + _
--------------(-3)-------------[-1]-------------[1]----------------(2,5)-------------
x∈(-∞;-3) U [-1;1] U (2,5;∞)
3
(2x-1)/(x+5)-1≥0
(2x-1-x-5)/(x+5)≥0
(x-6)/(x+5)≥0
x=6 x=-5
+ _ +
------------------(-5)---------------[6]-------------------
x∈(-∞;-5) U [6;∞)
4
(x-√2)(x+√2)(x²+2)/(x-2)(x²+2x+4)≤0
x²+4>0 U x²+2x+4>0 при любом х⇒
(x-√2)(x+√2)/(x-2)≤0
x=√2 x=-√2 x=2
_ + _ +
----------------[-√2]----------[√2]-----------------(2)------------------
x∈(-∞;-√2] U [√2;2)