The following is the draft english translation from a chapter of the book تيسير الوصول إلى الأصول (‘Teyseer al wusool Ila al-Usul’ - To make understanding Usul easy) by Sheikh Ata ibn Khalil Abu al-Rashta. Please refer to the original Arabic for accurate meanings:
When the evidences conflict and there is no advantage of one evidence over another; this is called equivalence (ta’aadul). Equivalence (ta’aadul) does not take place in the definite matters (qat’iyyaat) since there is no contradiction in them. It does not take place between a definite (qat’i) evidence and a speculative evidence (Zanni) because the qat’i evidence takes precedence over the zanni evidence. Also, it does not take place in the speculative matters (zanniyyaat) due to the legislative reality. Though logically there is nothing there to prevent it however it conflicts with the legislative reality. This because the speculative evidence, if it conflicts from all angles without the possibility of outweighing, then it is not possible to act upon them both or any one of them:
If one acts upon all of them while they are in complete equivalence then the coming together of opposites is not possible.
If we act upon one of them then the outweighing would be without a proper qualification since they are both equivalent in everything.
If we abandon acting upon them then the text is of no use, which is not possible for Allah.
Thus, equivalence does not exist in the evidences.
However, if the evidences conflict and one evidence has an advantage over another then this process is called tarjeeh (outweighing), where on evidence is deemed to be stronger than another in order to act upon it.
Tarjeeh is specific to the speculative evidences and does not occur in the definite issues because there is no contradiction in the definite matters.
The basis is to combine the evidences i.e. to use both evidences if possible because that is the basis. Otherwise one will have resort to tarjeeh. This is because the use of both evidences is better than neglecting one of them.
In what follows we shall mention some of the situations in which two evidences are used and then the process of outweighing.
Combining the evidences – using both evidences:
1. If the Messenger (saw) does an action and then does the opposite of that action then this means the action is mubah.
a) Acceptance of the gift
‘Iyaad b. Himaar narrated that the Messenger (saw) did not accept the gift of any kuffar after he had asked him: Have you embraced Islam? He (the kafir) said: No; He (saw) said: ‘I have been forbidden from taking the zabad of the Mushrikeen.’
It ha been authentically reported that the Messenger (saw) accepted the gift of the an-Najashi, Akidur duma, the Muqawqis, this is supported by the saying of ‘Aisha that the Messenger (saw) used to accept gifts and yutheeeb ‘alayh
The way they are reconciled is that we say the acceptance of gifts is mubaah.
b) At-Tabarani reported in ‘al-Awsat’ that: a funeral procession marrat ‘alah Ibn ‘Abbas and al-Hasab b. ‘Ali. One of them stood while the other sat. The one standing said to the one sitting: did not the Messenger of Allah (saw) stand? He said yes and sat down.’ From this we understand that it is permissible to stand or sit.
c) Az-Zuhri narrated that: ‘The Prophet (saw) sought the help of some Jews when he fought Khaybar and so he gave them a share of the booty.’ 
It has been narrated that ‘Aisha said: ‘The Prophet (saw) left for Badr. When he was in the lava field of the Wabra, a man of whom was mentioned bravery and energy reach/took over him, and the Sahabah of the Messenger (saw) were pleased when they saw him. When he reached him, he said: I came to join you and gain (booty) together with you. The Messenger of Allah (saw) said to him: Do you believe in Allah and His Messenger? He said: No. He said: Then return for I will never seek the assistance of a polytheist. She said: Then they went on until we were by the tree. The man reached him and said to him like what he said the first time. So the Prophet (saw) said to him like what he said the first time. He said: Return for I will never seek the assistance of a polytheist. He said: Then he returned and reached him at the desert. He said to him like what he said the first time: Do you believe in Allah and His Messenger? He said: Yes. So the Messenger of Allah (saw) said to him: Then set out’
In the fist hadith he accepted to use kuffar amongst the ranks of the Muslims under the banner Islam. And in the other hadith he refused. From this we understand that seeking the help of individuals from the Kuffar to fight for us among the ranks of the Muslims under the banner of Islam is permitted. This is different to seeking the help of the kuffar under their banner i.e. under the banner of the Kuffar. This is not allowed due to one saying of the Messenger (saw): ‘Do not seek light from the fire of the polytheists.’ The fire is a metonym (kinaayah) for the entity. So the tribe lights a fire as a sign of a declaration of war and seeking its light is to fight under its banner and this forbidden.
This understanding is supported by what has been reported about Abu Hameed as-Sa’idi that he said: ‘The Messenger of Allah (saw) went out until he passed Thaniyyat al-Wada’a when there appeared a squadron (kateeba) and he said: Who are these? They said: Banu Qaynuqa and they are the people (raht) of Abdullah bin Salam. He said: Have they embraced Islam? They said: No, they are on their religion. He said: Tell them to return. ‘Verily we do not accept assistance of the polytheists. And so they embraced Islam.’ So they used to go out to fight under their own banner.
As for when he (saw) sought the help of Jews in Khaybar when he fought them. They fought under the banner of the Muslims as established in the Seerah.
2. If the Messenger (saw) says something and does something contrary to that then the action is specific to the Messenger (saw) and the statement is a clarification for us.
a) ‘Umar narrated that the Prophet (saw) said: ‘The kiss is touching so make wudu for it.’
And ‘Aisha said: The Prophet (saw) used to kiss some of his wives and then pray without making wudu.’
So not making wudu due to kissing is specific to the Messenger (saw) and the request to make wudu is an address for us.
b) It has been narrated that Qays b. al-Haarith said: I embraced Islam whilst having 8 wives so I came to the Prophet (saw) and I mentioned that to him: He (saw) said: ‘choose 4 from them.’
It has been authentically narrated that the Messenger (saw) was married to 9 wives at the same time.
This indicates that marriage to more than four wives at the same time is specific to the Messenger (saw).’
3. When the Messenger (saw) says something and then says something which is contrary to it,
Reconciliation should be attempted in any manner possible:
The Messenger (saw) said: then lies will spread until a man gives witness before he is asked to give witness.’
He (saw) said: ‘Shall I tell you the best of witnesses. They said: Yes. He (saw) said: ‘That he should give witness before he is asked to give witness.’
The reconciliation of the hadiths is done in the following way:
The first hadith i.e. the person who gives witness before being asked to give witness and this is rebuked in the hadith: is regarding giving testimony to do with the rights of people before being asked to give witness. As for the second hadith, this is where it is praised. It is the person who rushes to give witness with regards to the right of Allah.
4. When we have a mujmal text and it is clarified by the Messenger (saw) by a statement and action which are contradictory such as when he (saw) said after the ayah of hajj was revealed: ‘Whosoever combines his Hajj to the ‘Umrah let him make one Tawaaf (circumbulation) and one Sa’i (running from Safa to Mawah).’
Also it has been reported that he (saw) combined them and made two Tawaafs and and two Sa’is. So the reconciliation will be as we clarified in chapter 4 in the section on Mujmal and Mubayyan.
5. The Muhkam and mutashaabih:
The muhkam is the foundation (Umm) of the mutashaabih: ‘In it there are Verses that are entirely clear (muhkamaat), they are the foundations of the Book and others which are ambiguous (mutashaabih)’ [3:7] If a text is muhakam and another is mutashaabih then the mutahsaabih is understood according to the Muhkam.
Fro example: He (swt) says: ‘…wash your faces and your hands (forearms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to the ankles.’ [5:6] The word ‘your feet’ is read as accusative (ie final consonant is read as a) or genitive (i.e. final consonant is read as I). Those who read it with an accusative case they understood it to be a conjunction to the washing ‘wa takoono majrooratul mujaawirq’. It can also be taken as a conjunction to wiping i.e. reading it as accusative means washing (muhkam) and reading it with an ‘i’ case means washing or wiping (mutashaabih). Therefore, reading it in the genitive should take the meaning of the accusative case and thus the feet should be washed.
 Tirmizi: 1504, Abu Dawud: 2657, Ahmad: 16835
 Tirmizi: 4/127, num: 1558
 Muslim: 1817, Tirmizi: 1558
 an-Nasaa`I : 5114, Ahmad: 11516
 Abu Dawud: 2356, Ibn Majah: 2822, ad-Darimi: 2385, Ahmad: 15203, 23250.
 Reported by Malik, ash-Shafi’I and al-Bayhaqi: 1/124
 Bukhari: 1972, an-Nasa`i: 170, Ibn Majah: 496
 Abu Dawud: 2241, Ibn Majah: 1952
 Anas narrated: The Prophet (saw) used to go round (have sexual relations with) all his wives in one night, and he had nine wives. ’ Bukhari: 260, 275, Muslim: 2656. Anas also narrated:….Bukhari: 1927, Tirmizi: 1136
 Muslim: 4602, Ahamd: 6836, Tirmizi: 2091, 2225, Ibn Majah: 2354
 Ibn Majah: 2355, Ahmad: 20698. And in Sahih Muslim the chapter on the best of witnesses.