I think that it depends on how close this person is to you. When it is a person not that close to you it's easier to forgive and forget than with a person close to you.
I'm not sure that you can forgive AND forget. Also when you did forgive and forget, and with that I mean the actually saying, it is hard to actually do it. When you have a bad day or you're in a bad mood and you meet the person you 'forgave', it is good possible that in a fight you bring it up again. So that means you didn't forget, but it still might be possible that you forgave.
So I would say you do 'forgive' and maybe try to forget as well, but deep inside you, you will always remember and never forget!