分类：教育/科学-学习帮助
问题：求x的取值范围 
回答：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<x<1
(2x-1)/(x^2-1)<m ==>(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<x<1
综合:1): 2): 3): 4):
x<-(√7+1)/2 
(1-√3)/2<x≤1
x>(√7-1)/2