Greetings!
It is actually possible to forgive adultery, however, it is not the best thing to do. Why?
First of all, I stated it is possible because it is feasible, it is probable, you know? We all know plenty of cases in which that has happened, either if it is a woman who forgives a man, or a man who forgives a woman; we have all witnessed those cases.
Now, why do I state that it is "not the best thing to do"? Because of the act of cheating itself. Cheating is never an accident. It is a choice. Cheaters often ask for forgiveness because they know for sure that their partners have something that the person they cheated with, doesn't. They have stability, and in many cases, they have children in common, which makes the situation a little bit of more advantage for them, and when they get their forgiveness, they have been implicitly given permission to do it again...
But I still haven't defined why it is a mistake to forgive a cheater: It is a mistake, because the person who cheats has already violated the trust the other person granted him/her, and nobody deserves to be betrayed, especially because who cheats once, can cheat twice, and even more if allowed.
No one should lay down next to a person who has betrayed him/her. That's not healthy, or fair.
P.S: I have based my arguments on general notions and truths, because if I had based them on my personal experience (from my family and my own), I had extended myself too much, besides, I wanted to keep it as objective as possible.