不等式8/X^-9

题目

不等式8/X^-9<=1/IXI的解集

答案

|x|>0
所以8|x|/(x^2-9)<=1
(8|x|-x^2+9)/(x^2-9)<=0
(x^2-8|x|-9)/(x^2-9)>=0
x<=0
则(x^2+8x-9)/(x^2-9)>=0
(x+9)(x-1)/(x+3)(x-3)>=0
x<=-9,-3<=x<=1,x>=3
且x<=0,分母不等于0
所以x<=-9,-3x>0
则(x^2-8x-9)/(x^2-9)>=0
(x-9)(x+1)/(x+3)(x-3)>=0
x<=-3,-1<=x<=3,x>=9
且x>0,分母不等于0
所以0所以-9<=x,-3=9