Matthew 19:7-9
7 They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away?
8 He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so.
9 And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.
The term put away does not mean divorce.
Apoluo: Put away. Used 89 times in the NT, not once as divorce.
Apostasion: Divorce, divorce certificate. Used 3 times in the NT, not once by Jesus.
In ancient times the pharisees would put away their wives for reasons other than fornication, without a divorce certificate. Why would the pharisees do this?
1. The ketubah (sort of like a prenuptial agreement) was only payable to the wife if she had the divorce certificate in hand.
2. Without the divorce certificate the woman wasn't able to remarry so the pharisee could take her back and still be within the Deut. 24 law.
Jesus is telling the pharisees their manipulation of the law, the putting away and marrying another for reasons other than fornication, will be judged as adultery.