So what happens if your ex-girlfriend broke up with you and dated someone else, and now wants to get back with you? Should you eliminate her from your life or should you get back with your ex?
First, you have to decide if you actually want to take her back. If she's interested in coming back, she was probably the one who ended the relationship in the first place. Look past the fact that you still have feelings for her and decide if you still want things to work out.
Before you decide you want to take her back, figure out it the two of you can make things work. Sometimes it's easy to forgive, especially when you are lonely, but don't forget what she did to you and hurt you. If she left you because she was interested in someone else she's likely to do it again whenever someone else comes along she thinks is interesting. Examine all the possible signs of a bad relationship and decide whether you can truly forgive her and if you can trust her.
Get the whole story. Let your pride and ego aside and ask yourself if you did anything to cause her to leave. Is it possible you didn't realize you were neglecting her and making her feel like she was being taken for granted? If she left because of something you've done, examine if anything has changed that can make the relationship work.
If you did, there maybe a chance you both can work things out if she's truly serious about committing to the relationship. If not, the relationship may fall apart again and you might be better off not getting involved with her again.
Not many people are that fortunate to get a second chance. If you do take her back, you must let the past go and work on the present and the future.