While this study shows that divorce has consequences for everyone involved, it is in no way condemning people who have divorced. We need to convey that they have been forgiven in Christ and encourage them to put the divorce behind them and press on in Christ. If they remarry, they need to know we do not condemn, disparage, or belittle the new marriage in any way but rather encourage them to devote themselves to it.

The following Biblical passages under consideration have been offered by some as grounds for divorce:

But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
Matthew 5:32

This passage is explained by some as saying that if one of the marriage partners, in this case the wife, commits fornication, divorce is therefore sanctioned.
Divorce therefore is legal and biblically allowed only when there is fornication by one of the marriage partners.

Was The Lord Jesus really saying that it was all right to divorce under these circumstances?

My understanding of the passages does not uphold this view. I understand the passage as not providing substantiation for divorce, but rather, embellishing on the fact that divorce causes adultery.

I understand The Lord Jesus to be saying that if the wife who has committed fornication by having sexual relations with someone other than her husband is divorced; she can not be made to commit adultery by marrying someone else because she has already committed adultery.
Under any other circumstances a wife that is divorced by her husband and then marries someone else is caused to commit adultery.
Also whosoever she marries commits adultery with her.

Fornication is not an exemption that allows the dissolution of a marriage but rather, unless adultery was preexistent, remarriage after divorce causes adultery.

Biblically only death dissolves the marriage bond, but God made provision under the law for divorce. This was put in place because of the sinfulness of mankind.
Jesus explained why God allowed divorce.
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. Matthew 19:8
The provision for divorce in Deuteronomy 24 permitted divorce if a woman commited uncleanness, which included adultery and fornication. Verse 2 even allows a wife who is divorced to remarry.
24:1 When a man hath taken a wife, and married her, and it come to pass that she find no favor in his eyes, because he hath found some uncleanness in her: then let him write her a bill of divorcement, and give it in her hand, and send her out of his house.

24:2 And when she is departed out of his house, she may go and be another man's wife.

24:3 And if the latter husband hate her, and write her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house; or if the latter husband die, which took her to be his wife;

24:4 Her former husband, which sent her away, may not take her again to be his wife, after that she is defiled; for that is abomination before the LORD: and thou shalt not cause the land to sin, which the LORD thy God giveth thee for an inheritance. Deuteronomy 24:1-4
Christ was not applying Deuteronomy 24 in allowing divorce because the wife commited fornication in Matthew 19 below. Rather than sanctioning divorce, He was detailing the consequences of divorce. Divorce compounds and generates adultery.

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.
Matthew 19:9

A cursory reading of this passage would lend to the interpretation that the husband who divorces his wife on the grounds of fornication would not commit adultery by remarriage. It would appear as though these circumstances would afford an approved divorce. This however is not the case, as the phrase (and shall marry another) applies to both the husband, and the wife.

The husband that (shall marry another) shall commit adultery because divorce does not dissolve marriage. The divorced wife that performed fornication while married, if she (shall marry another), can not commit adultery solely by this new marriage since she has already committed adultery.

The next husband that marries the divorced wife is also caused to commit adultery.

Whosoever shall put away his wife, and marry another, committeth adultery against her.
Mark 10:11

And if a woman shall put away her husband, and be married to another, she committeh adultery.
Mark 10:12

In these verses both the divorcing husband and wife fall into adultery.

Whosoever putteth away his wife, and marrieth another, committeth adultery: and whosoever marrieth her that is put away from her husband committeth adultery.
Luke 16:18

Again there is no exception allowed in this passage to relieve the charge of adultery; whether husband or wife, if they divorce their spouse and marry another, they commit adultery.
Also, the new marriage partner of either husband or wife is likewise charged with committing adultery.

Under the law only death broke the marriage bond.

Know ye not, brethren,(for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth?
For the woman which hath an husband is bound by the law to her husband so long as he liveth; but if the husband be dead, she is loosed from the law of her husband.
So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man.
Romans 7:1-3
We are under grace, and in Christ Jesus, when we fail and sin we have complete forgivesness.
In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace; Ephesians 1:7

The exhortation for us, is to take a higher view of marriage, and minister grace to people who divorce.

What therefore God hath joined together, let no man put asunder.
Matthew 19:6