The following is an excerpt from page 2547 of the ESV Study Bible article titled Divorce and Remarriage:
What should be done if someone has been divorced for other reasons than those given in the Bible and then has married someone else? Jesus says that in such a case the person has committed “adultery” (Matt. 19:9), so the marriage began with adultery. But when Jesus says, “and marries another” in the same verse, he implies that the second marriage is in fact a true marriage. Jesus does not say, “and lives outside of marriage with another” (which was possible, see John 4:18), but “and marries another.” Therefore, once a second marriage has occurred, it would be further sin to break it up, for it would be destroying another marriage. The second marriage should not be thought of as continually living in adultery, for the man and woman are married to each other, not to anyone else. The responsibility of the husband and wife in such a case is to ask God for his forgiveness for previous sin, and then for his blessing on the current marriage, and to strive to make the current marriage a good and lasting one.