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X²-3x=a (a-2)/(a+2)+(a+16)/a≥0 (a²-2a+a²+16a+2a+32)/a(a+2)≥0 (2a²+16a+32)/a(a+2)≥0 2(a+4)²/a(a+2)≥0 a=-4 a=-2 a=0 + + _ + ---------[-4]------------(-2)----------(0)----------- a<-2 U a>0 x²-3x<-2 U x²-3x>0 x²-3x+2<0 U x²-3x>0 (x-1)(x-2)<0 U x(x-3)>0 1<x<2 U x<0 U x>3 x∈(-∞;0) U (1;2) U (3;∞)
Answers & Comments
(a-2)/(a+2)+(a+16)/a≥0
(a²-2a+a²+16a+2a+32)/a(a+2)≥0
(2a²+16a+32)/a(a+2)≥0
2(a+4)²/a(a+2)≥0
a=-4 a=-2 a=0
+ + _ +
---------[-4]------------(-2)----------(0)-----------
a<-2 U a>0
x²-3x<-2 U x²-3x>0
x²-3x+2<0 U x²-3x>0
(x-1)(x-2)<0 U x(x-3)>0
1<x<2 U x<0 U x>3
x∈(-∞;0) U (1;2) U (3;∞)