- 求x的取值范围
- 2x-1>m(x^2-1) -2≤m≤2
1):x=1 2-1=1>0
2):x=-1 -3<0 (设去)
3):x^2-1>0 ==>x^2>1 ==>x<-1 or x>1
(2x-1)/(x^2-1)>m ==>(2x-1)/(x^2-1)>-2 ==>(2x-1)/(x^2-1)+2>0 ==>
(2x^2+2x-3)/(x^2-1)>0 ==>[x-(√7-1)/2,x+(√7+1)/2]/(x^2-1)>0 ==>
x>(√7-1)/2 or x<-(√7+1)/2
4):x^2-1<0 ==>x^2<1 ==>-1(2x-1)/(x^2-1)<2 ==>(2x-1)/(x^2-1)-2<0 ==>
(-2x^2+2x+1)/(x^2-1)<0 ==>(2x^2-2x-1)/(x^2-1)>0 ==>
[x-(√3+1)/2,x-(1-√3)/2]/(x^2-1)>0 ==>[x-(√3+1)/2,x-(1-√3)/2]<0 ==>
(1-√3)/2(√7-1)/2