How are different hadiths reconciled?

Question:
Reconciling differing hadiths?

Answer:
The apparent view, from the perspective of the narrators' memorization, is based on the rule: if a narrator adds to the text, his addition is accepted. This is a rule. Since narrators differ, if some add to what others have, the addition is accepted, provided the one who added is trustworthy. Even the news of people today, when an incident occurs... their news, and the rule is that the addition is accepted if it is narrated by a trustworthy person.
Q: What if the narrator without the addition is more trustworthy?
The Shaykh: Even if so, as long as the addition does not contradict or conflict, it does no harm. The Hafiz says in al-Nukhba: "The addition of their narrator (i.e., of the sahih and hasan) is accepted, unless it conflicts with one who is more trustworthy." As long as it does not conflict, this is the case. One said one hundred, and the other said one hundred and twenty. There is no debate about this; the bottom line is that it was omitted by the one who said one hundred because he did not notice the addition, while the other memorized it. Similarly, one of them omitted the camels and sheep, while the other memorized the addition.