Tirmidhi

English Commentary: 1؎ :
The majority of scholars have deduced from this hadith that a single circumambulation (tawaf) is sufficient for the one performing qiran (combining Hajj and Umrah without exiting the state of ihram).
And what is meant by this is the 'tawaf between Safa and Marwah', that is, the sa'i, and not the circumambulation (tawaf) of the Ka'bah itself,
because the Prophet sallallahu alayhi wa sallam, during the Farewell Pilgrimage (Hajjat al-Wada'), performed the tawaf of the Ka'bah for Umrah as well,
and on the Day of Sacrifice (Yawm al-Nahr) also performed the Tawaf al-Ifadah,
however, he did not perform the sa'i between Safa and Marwah during the Tawaf al-Ifadah.
(See: Sahih Muslim, Book of Hajj, Chapter No. 19) Note:

(In the chain of narration, both Hajjaj ibn Arta'ah and Abu al-Zubayr are mudallis narrators, and the narration is in the form of 'an'anah,
but on account of corroborating narrations (mutaba'at), this hadith is considered sahih li ghayrihi [authentic due to supporting evidence].)

Hadith Commentary: Benefits and Issues: The noble Companions (radi Allahu anhum ajma'in) who performed Qiran Hajj with the Messenger of Allah (sallallahu alayhi wa sallam) performed the sa'i along with the Tawaf al-Qudum, and then did not perform the sa'i again after the Tawaf al-Ifadah. If they were unable to perform the Tawaf al-Qudum, then they performed the sa'i after the Tawaf al-Ifadah. However, those who were performing Tamattu' performed the sa'i again after the Tawaf al-Ifadah. The Messenger of Allah (sallallahu alayhi wa sallam) and other affluent Companions were Qarin, therefore, they performed only one sa'i. The Prophet (sallallahu alayhi wa sallam) performed three tawafs: Tawaf al-Qudum, Tawaf al-Ifadah, and Tawaf al-Wada', but performed only one sa'i.

1895. Commentary: Qarin refers to a person who has entered into the state of ihram for both ‘umrah and hajj together.

Here, by "tawaf" (circumambulation), "sa'i" (ritual walking between Safa and Marwah) is intended. The one performing only Hajj will, by consensus, perform only one sa'i, whether he does it with the tawaf al-qudum (arrival circumambulation) or with the tawaf al-ziyarah (visitation circumambulation). There is no sa'i with the tawaf al-wada' (farewell circumambulation). According to the majority of scholars, the one performing tamattu' (combining 'umrah and Hajj with a break in between) must perform a separate sa'i for 'umrah and a separate one for Hajj. Thus, he will perform sa'i twice. Only Imam Ahmad has a differing opinion that one sa'i is sufficient for the mutamatti' (one performing tamattu'). However, in light of the ahadith, this position is considered weak. The main difference of opinion concerns the qarin (one combining 'umrah and Hajj without a break). According to the Hanafis, the qarin will also perform sa'i twice: once for 'umrah and once for Hajj. However, Imam Malik, Imam Shafi'i, and Imam Ahmad rahimahumullah consider one sa'i sufficient for the qarin, as is established from the aforementioned hadith, and this is the stronger opinion. And Allah knows best.