1)
(x+17)/(x+3)≥3 ОДЗ: x+3≠0 x≠-3
(x+17)/(x+3)-3≥0
(x+17-3*(x+3))/(x+3)≥0
(x+17-3x-9)/(x+3)≥0
(8-2x)/(x+3)≥0
-2*(x-4)/(x+3)≥0 |÷(-2)
(x-4)/(x+3)≤0
-∞_____+______-3_____-_____4______+_______+∞
x∈(-3;4].
Ответ: xmax=4.
2)
(x+6-x²)/(x²+2x+1)≤0
-(x²-x-6)/(x+1)²≤0 |÷(-1)
(x²-x-6)/(x+1)²≥0 ОДЗ: x+1≠0 x≠-1
(x²+2x-2x-x-6)/(x+1)²≥0
(x*(x+2)-3*(x+2))/(x+1)²≥0
(x+2)*(x-3)/(x+1)²≥0
-∞_____+____-2____-_____-1_____-_____3______+______+∞
x∈(-∞;-2]U[3;+∞).
3)
(x²-4x)*(x²-6x+9)≤0
x*(x-4)*(x-3)²≤0
-∞_______+_______0______-_______4________+_______+∞
x∈[0;4]
Ответ: xmax=4.
4)
(3x-x²)*(x²+2x-8)>0
x*(3-x)*(x²+2x+2x-2x-8)>0
x*(3-x)*(x²+4x-2x-8)>0
x*(3-x)*(x*(x+4)-2*(x+4))>0
x*(3-x)*(x+4)*(x-2)>0
-∞___-____-4____+___0___-____2___+____3___-____+∞
x∈(-4;0)U((2;3).Ответ: xmax=-1.