The one translation says, sexual immorality,
another translation says fornication.
There was no difference of opinion about sexual immorality as unfaithfulness in marriage between Jesus and the Pharisees. That is a sin against the seventh commandment. Jesus does not need to talk about that. Jesus is talking about different reasons for divorce. Reasons, which according to Jewish tradition fell between the parameters of the law, and where a certificate of divorce was arranged according to the rules of the law.
In Jewish tradition there were different thoughts about divorce. The reason for divorce (the man is unhappy with his wife for some reason—Deuteronomy 24:1–22 says that he has found some indecency in her) was interpreted in different ways. According to the strict teachers of the law, it could only be unchastity or debauchery. But for the more liberal teachers of the law, this was open to a wider interpretation.
Jesus declares that both the man and the woman are guilty of adultery in a marriage with a divorced woman. That is an intriguing pronouncement, because this was not against the law as seen in those days. When, with a divorce, a certificate of divorce was issued, no laws had been broken according to Jewish law.
Jesus does not introduce new rules of law about divorce and re-marriage but wants to explain the great seriousness of sin, in this regard. Sin cannot be made into something wholesome by following the rule(s) of law, but one needs to be aware of one’s guilt and ask for grace and forgiveness. The only sacrifice, with which sins are made whole again, is the sacrifice of Jesus. He is the fulfillment of the law.
32 But I say to you that everyone who divorces his wife, except on the ground of sexual immorality, makes her commit adultery, and whoever marries a divorced woman commits adultery.