Why does Matthew mention the exception to divorce but Mark and Luke don’t?

Answer:

Each gospel account was written to different audiences with different purposes. None give a complete account of what Jesus did while on earth because as John points out, "And there are also many other things that Jesus did, which if they were written one by one, I suppose that even the world itself could not contain the books that would be written. Amen" (John 21:25). With such a wealth of information, each author with the guidance of the Holy Spirit selected the best subset for their target audience. Matthew appears to be aimed at the Jews. Mark was written for the Romans. Luke was also aimed at Gentiles, with the Greeks particularly in mind. John was written for Christians.

While there are overlaps, the repetition is minimal. If something is discussed in detail in one account, it may only be mentioned lightly in another. It appears that the Holy Spirit planned to keep each book as small as necessary by relying on the fact that you can get the details in at least one book.

So Matthew did mention the exception clause twice (Matthew 5:32 and Matthew 19:9). This was a subject being debated by the Jews and it was of particular importance to that audience. Mark and Luke mention the general rule because their audiences were not interested in parsing the Law of Moses. It was more important to get the main rule across to the Gentiles: Marriage is for life! You will notice that John doesn't even bother mentioning the discussions about divorce because this ought to be less of an issue for Christians who already know Christ's teachings about marriage.