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Dear Benedicta,
I would say that people are in disagreement when they have different opinions or have personal issues with each other.
For the first case I would say that a good analysis would tell you what you need to do - the solution can be about team building or breaking them apart or anything in between.
If it's the second case then you may be able to make them work on the issues themselves, since involving yourself in their personal life is not a good idea.
Hope this helps