For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Matt. 5:32 is about the woman causing her own adultery. The man sent her away without a certificate of divorce. Since this is an unlawful divorce they are still married. For her to get married again would cause her to comment adultery but if she committed fornication she caused herself to commit adultery. In verses 31 and 32 two words are translated as divorce, one a lawful divorce with a certificate, the other unlawful without a certificate. The use of two words for divorce is what causes misunderstanding.