Excuse but then Deut talking about divorce as nothing to about adultery. Also look into Hebrew. Put away is what is talked about not divorce for put away and divorce aren't the same thing . Like at Deut She got divorce by her husband to become a another man's wife
The first mention of divorce is found in Deuteronomy 24:1,2 , When a man hath taken a wife, and married her, and it come to pass that she find no favour 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. And when she is departed out of his house, she may go and be another man's wife.
Jesus teaching on divorce -
When you understand the difference between the Hebrew words keriythuwth (divorce) and shalach (the putting out or sending forth), then you can fully understand Jesus teaching on divorce in Matthew chapter five.
In Matthew 5:31 Jesus said, It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement. He is obviously quoting from Deut 24:1 when He mentions the two different components of divorce.
Again if marrying an divorce woman is a sin then you must reject deut for it give the woman a right to become a another man's wife. Jesus did not change god's law or divorce and Paul didn't even
I believe the very next verse derails what you say that Jesus has taught.
Matthew 5:31 It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement: 32 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.
Jesus made the reference as you had said to Deuteronomy 24:1-2, but He raised the bar as to what the New Covenant shall entail.
He gives another example in Matthew 5:33-37 of referring to the old law of how Jews practised in performing their oaths but declared not to make oaths at all, not even by swearing which some of the Jews had done to declare the sincerity of finishing that oath. Jesus said it was of evil now because we are not under the law to effect changes in us in doing God's work in us. Only God can do God's work in us which is why the just shall live by faith which is what Matthew 5:36 was refering to as we cannot make one hair white or black.
So making a promise or a commitment to follow Him is of the flesh whereas living by faith in Him & all His promises to us that He will enable us to follow Him is how we get to know Him & the power of His resurrection when we see Him living in us for us to be living the christian life.
So Jesus reference to divorcing the spouse and marrying a divorced spouse as committing adultery now is to point out the necessity to acknowledge that as a sin against God in need of forgiveness, and for those that are contemplating a divorce, to go before that throne of grace for help to have the love of Christ to love one another as they ought to.
Paul gave the guideline to be seperated, and by praying and fasting to come together again lesthe devil tempt the couple with their incontency.
1 Corinthians 7:4 The wife hath not power of her own body, but the husband: and likewise also the husband hath not power of his own body, but the wife. 5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency.
Here is a commandment from the Lord.
10 And unto the married I command, yet not I, but the Lord, Let not the wife depart from her husband: 11 But and if she depart, let her remain unmarried or be reconciled to her husband: and let not the husband put away his wife.
In the event of an unbelieving spouse: Paul speaks and not the Lord:
12 But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away. 13 And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him. 14 For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy. 15 But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace. 16 For what knowest thou, O wife, whether thou shalt save thy husband? or how knowest thou, O man, whether thou shalt save thy wife? 17 But as God hath distributed to every man, as the Lord hath called every one, so let him walk. And so ordain I in all churches.
Verse 15 would suggest that when it comes to both believing spouse, the marriage bondage remains.
What happens to those that have divorced and remarried?
Hebrews 13:3 Remember them that are in bonds, as bound with them; and them which suffer adversity, as being yourselves also in the body. 4 Marriage is honourable in all, and the bed undefiled:
but whoremongers and adulterers God will judge. 5 Let your conversation be without covetousness; and be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee.
Not my place to judge. That does not mean they are not saved. God will judge His children.
Matthew 5:19 Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven.
I do wonder how God will judge those that breaks one of the least commandments BUT do not teach others so as a form of repentance, but we shall see, but at no time am I advocating using God's grace to sin.
For those going through difficult times in their marriage, best turn to the One that joined them together.
Philippians 4:11 Not that I speak in respect of want: for I have learned, in whatsoever state I am, therewith to be content. 12 I know both how to be abased, and I know how to abound: every where and in all things I am instructed both to be full and to be hungry, both to abound and to suffer need. 13 I can do all things through Christ which strengtheneth me.
1 Peter 2:19 For this is thankworthy, if a man for conscience toward God endure grief, suffering wrongfully. 20 For what glory is it, if, when ye be buffeted for your faults, ye shall take it patiently? but if, when ye do well, and suffer for it, ye take it patiently, this is acceptable with God. 21 For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps: 22 Who did no sin, neither was guile found in his mouth: 23 Who, when he was reviled, reviled not again; when he suffered, he threatened not; but committed himself to him that judgeth righteously: 24 Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed. 25 For ye were as sheep going astray; but are now returned unto the Shepherd and Bishop of your souls.
must be properly differentiated to clear up mistaken notions about divorce and remarriage. The Hebrew word keriythuwth translated “divorce” in Deuteronomy 24:1 is found in only two other locations: Isaiah 50:1, which describes Yahweh’s future divorce of the House of Judah, and Jeremiah 3:8, which describes Yahweh’s past divorce of the House of Israel. Keriythuwth, translated “divorce,” is a specific term, and in all three instances it is used in conjunction with the term “bill,” “writ” or “certificate.” On the other hand, the Hebrew word shalach, translated “send her out” or “put away,” is a common term used nearly one thousand times in the Old Testament. While it is true that the term “put away” – the final step in the divorce process – is sometimes used to represent divorce, women can and often were put away without being divorced. 
