不等式|x-1|+1/(x+1)>x-1+1/(x+1)的解集是?小女子感激涕零!

Question

不等式|x-1|+1/(x+1)>x-1+1/(x+1)的解集是?
小女子感激涕零!

Answer 1

|x-1|+1/(x+1)>x-1+1/(x+1)
转化为：|x-1>x-1
|①当x>1时,x-1>x-1,无解
②当x<1时,1-x>x-1,解得x<1
x+1≠0 解得x≠-1
综上x<1且x≠-1