1
(3x-15)/(x²+5x-14)≥0
3x-15=0⇒3x=15⇒x=5
x²+5x-14=0
x1+x2=-5 U x1*x2=-15⇒x1=-7 U x2=2
_ + _ +
---------------(-7)-----------(2)----------[5]------------
x∈(-7;2) U [5;∞)
2
(x-1)/(x²+4x+2)<0<br>x-1=0⇒x=1
x²+4x+2=0
D=16-8=8
x1=(-4-2√2)/2=-2-√2 U x2=-2+√2
_ + _ +
---------------(-2-√2)-------------(-2+√2)------(1)------------
x∈(-∞;-2-√2) U (-2+√2;1)
3
(x²+2x-8)/(x²-2x-3)>0
x²+2x-8=0
x1+x2=-2 U x1*x2=-8⇒x1=-4 U x2=2
x²-2x-3=0
x1+x2=2 U x1*x2=-3⇒x1=-1 U x2=3
+ _ + _ +
-----------(-4)---------(-1)--------(2)--------(3)----------
x∈(-∞;-4) U (-1;2) U (3;∞)
4
(x-5)(2^1/(x-1) +0,2)/(x+2)≤0
2^1/(x-1) +0,2>0 при любом х,кроме х=1⇒
(x-5)/(x+2)≤0,x≠1
x=5 x=-2
+ _ +
-------------(-2)----------[5]----------
x∈(-2;1) U (1;5]