If someone commits adultery, what would God want the faithful spouse to do?

I was talking with a friend about this and she told me God would want the spouse to work it out. I don't know if I fully believe this only because God does want us to forgive and forget...I'm not saying that He doesn't, and yes, if we are fully capable of complete forgiveness, then it is worth working out. The thing that I keep considering is when Jesus was addressing the pharisees about divorce also when Paul was talking about abandonment...but anyway, does anyone have any scriptural information on this topic? Thanks in advance.