The question is actually two questions. One involves divorce and the other remarriage. It is clear that, without exception, the scriptures treat remarriage of a divorced person as adultery. So it would therefore seem logical that remarriage of divorced people can never be permitted. But is divorce permitted? In the Matthew 5 verse it seems that Jesus is saying that a divorce is only permitted for adulterous behavior, a change in the Mosaic Law to be sure. Besides death, adultery is the only act that can break the covenant relationship of marriage. So the Mosaic Law was actually more liberal than what Jesus taught and Jesus states as such. But Jesus also adds that it wasn’t always that way. In Mt 19:3 we find the following:
"3And Pharisees came up to him and tested him by asking, “Is it lawful to divorce one’s wife for any cause?” 4 He answered, “Have you not read that he who made them from the beginning made them male and female, 5 and said, ‘For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh’? 6 So they are no longer two but one flesh. What therefore God has joined together, let not man put asunder.” 7 They said to him, “Why then did Moses command one to give a certificate of divorce, and to put her away?” 8 He said to them, “For your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so. 9 And I say to you: whoever divorces his wife, except for unchastity, and marries another, commits adultery.” [Mt 19:3-9]
That passage creates a problem though. When is the adultery committed? Is it committed in divorcing one’s spouse or is it committed in remarrying? Fortunately Mark’s gospel clarifies the matter. Mark 10:2-12 records the event as follows:
"2 And Pharisees came up and in order to test him asked, “Is it lawful for a man to divorce his wife?” 3 He answered them, “What did Moses command you?” 4 They said, “Moses allowed a man to write a certificate of divorce, and to put her away.” 5 But Jesus said to them, “For your hardness of heart he wrote you this commandment. 6 But from the beginning of creation, ‘God made them male and female.’ 7 ‘For this reason a man shall leave his father and mother and be joined to his wife, 8 and the two shall become one flesh.’ So they are no longer two but one flesh. 9 What therefore God has joined together, let not man put asunder.” 10 And in the house the disciples asked him again about this matter. 11 And he said to them, “Whoever divorces his wife and marries another, commits adultery against her; 12 and if she divorces her husband and marries another, she commits adultery.” [Mr 10:2-12]
Luke 16:18 is in agreement with Mark as is Romans 7:3. Romans 7:3 in fact stresses the point that the adultery is committed in the remarriage or cohabitation:
“Accordingly, she will be called an adulteress if she lives with another man while her husband is alive. But if her husband dies she is free from that law, and if she marries another man she is not an adulteress.” [Romans 7:3]