Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
quran:2:230

And if he has divorced her ˹for the third time˺, then she is not lawful to him afterward until ˹after˺ she marries a husband other than him. And if the latter husband divorces her ˹or dies˺, there is no blame upon the woman and her former husband for returning to each other if they think that they can keep ˹within˺ the limits of Allah. These are the limits of Allah, which He makes clear to a people who know.  

If he, the husband, divorces her, after the two utterances ˹of divorce˺; she shall not be lawful to him after that, after the third ˹utterance of˺ divorce, until she marries another husband, who has sexual intercourse with her, as reported by the two Shaykhs ˹Bukhārī and Muslim˺. If he, the second husband, divorces her, then neither of them would be at fault, that is, the woman and her first husband, to return to each other, in wedlock, after the completion of the waiting period, if they think that they will maintain God’s bounds. Those, matters mentioned, are God’s bounds, which He makes clear to a people who have knowledge, ˹a people who˺ reflect.
القرآن:٢:٢٣٠

فَإِنْ طَلَّقَهَا فَلَا تَحِلُّ لَهُ مِنْ بَعْدُ حَتَّىٰ تَنْكِحَ زَوْجًا غَيْرَهُ ۗ فَإِنْ طَلَّقَهَا فَلَا جُنَاحَ عَلَيْهِمَا أَنْ يَتَرَاجَعَا إِنْ ظَنَّا أَنْ يُقِيمَا حُدُودَ اللَّهِ ۗ وَتِلْكَ حُدُودُ اللَّهِ يُبَيِّنُهَا لِقَوْمٍ يَعْلَمُونَ  

{فإن طلقها} الزوج بعد الثنتين {فلا تحل له من بعد} بعد الطلقة الثالثة {حتى تنكح} تتزوج {زوجا غيره} ويطأها كما في الحديث رواه الشيخان {فإن طلقها} أي الزوج الثاني {فلا جناح عليهما} أي الزوجة والزوج الأول {أن يتراجعا} إلى النكاح بعد انقضاء العدة {إن ظنا أن يقيما حدود الله وتلك} المذكورات {حدود الله يُبَيِّنها لقوم يعلمون} يتدبرون.