My ex-girlfriend wants me back, but I don't know what to do?

I apologize for this being long. I had been dating this girl for just short of 3 months. She broke up with me saying that we weren't compatible and that it wasn't working out. Two days later, she regrets it and says that she wants me back. This is the third time something like this happened. The first time, she did some sexual things with two guys, which she later told me and apologized. I don't know whether I should take her back or not. I still love her and want to be with her, but at the same time I don't want to be stuck in a failing relationship. She said that she needs me to "fill a hole" in her heart. I'm torn and I have no idea what to do :-(