Hi Didn't Harper used to live with Alex how come she doesn't anymore?

No, she still does. She lives in her basement. Maybe you're referring to that episode when Harper wasn't there. But the beginning Theresa and Jerry were complaining that Harper were visiting her parents for the weekend. I hope that clears your confusion (:

The person above me is exactly right. She moved in with the Russos in 'Dollhouse', and was with them for the next ten-ish episodes, until she went to visit her parents in 'Alex's Logo'. She was back with them in 'Max's Secret Girlfriend' onward. As far as I remember, though, she wasn't in 'Dude Looks Like Shakira', but I don't think that that was because she moved out or anything.