不等式

2x2-x-1

(x-1)|x|

≥0等价于

(x-1)(2x+1)

(x-1)|x|

≥0

∴x≠0且x≠1且2x+1≥0

∴x＞1或0＜x＜1或-

1

2

≤x＜0

∴不等式

2x2-x-1

(x-1)|x|

≥0的解集为{x|x＞1或0＜x＜1或-

1

2

≤x＜0}

故答案为：{x|x＞1或0＜x＜1或-

1

2

≤x＜0}