1
1/x+1/x²-6/x³>0
(x²+x-6)/x³>0
(x+3)(x-2)/x³>0
x=-3 x=2 x=0
_ + _ +
--------------(-3)----------(0)------------(2)-------------
x∈(-3;0) U(2;∞)
2
(x-1)/x-(x=1)/(x-1)-2<0<br>(x²-2x+1-x²-x-2x²+2x)/x(x-1)<0<br>(1-2x²)/x(x-1)<0<br>x=-1/√2 x=1/√2 x=0 x=-1
_ + _ + _
---------------(-1)--------(-1/√2)------(0)--------------(1/√2)----------------
x∈(-∞;-1) U (-1/√2;0) U (1/√2;∞)
3
2/(x-2)-2/(x+1)-3/(x-2)²/(x+1)(x-2)²<0<br>(2x²-2x-4-2x²+8x-8-3x-3)/(x+1)(x-2)²
(3x-15)/(x+1)(x-2)²<0<br>x=5 x=-1 x=2
+ _ _ +
-------------(-1)---------------(2)----------------(5)--------------
x∈(-1;2) U (2;5)
4
1+2/(x-1)-6/x>0
(x²-x+2x-6x+6)/x(x-1)>0
(x²-5x+6)/x(x-1)>0
(x-3)(x-2)/x(x-1)>0
x=3 x=2 x=0 x=1
+ _ + _ +
---------------(0)--------(1)------------(2)-------------(3)-------------
x∈(-∞;0) U (1;2) U (3;∞)
5
-15/x²-16/x^4+1<0<br>(-15x²-16+x^4)/x^4<0<br>x^4-15x²-16=0
x²=a
a²-15a-16=0
a1+a2=15 U a1+a2=-16
a1=-1 a2=16
(x²+1)(x-4)(x+4)/x^4<0<br>x²+1>0при любом х
x=4 x=-4 x=0
+ _ _ +
------------(-4)-----------(0)----------------(4)--------------
x∈(-4;0) U (0;4)