The following passages are sometimes placed in opposition:

A "problem" is alleged in that Matthew includes an additional phrase, "except for marital unfaithfulness", not found in Mark.

Some critics say that the phrase was added to reflect the needs of the early church; and maybe it was, but that by no means requires that Jesus never added that qualification on His own at some point, perhaps in a different context or teaching. Matthew could simply have conflated two of Jesus' separate teachings, which is no crime.

But the most likely reason for the difference is that Matthew was spelling out what Luke and Mark leave implicit within the social context. The divorce debate in Jewish circles in Jesus' day pitted the followers of Hillel against those of his rival, Shammai. Hillel took a more liberal view, permitting divorce in a variety of circumstances (even if the wife spoiled a meal!); Shammai, only in the case of adultery. In both Jewish and Greco-Roman society, Blomberg notes in his commentary on Matthew, "divorce and remarriage were universally permitted and often mandatory following adultery." [292] Hagner's commentary on Matthew [549] adds: "Rabbinic Judaism required a husband to divorce an unfaithful wife." (m. Sota 5:1, m. Yebam 2:8; also Qumran literature, 1QapGen 20:15; Marcus Bockmuehl notes these passages and ties it not to Hillel and Shammai, but to halakhah on Deut. 24:4; neverthless his point is the same: the exception was presupposed -- Marcus Bockmuehl, "Mt. 5:32, 19:9 in Light of Pre-Rabbinic Halahkah," NTS 35 (1989), 291-5) In other words, both sides agreed on the exception which Matthew adds, and by the same token, Jesus could certainly have safely presupposed it without any fear of misunderstanding.

See Doug Krueger try to overcome this answer here.