It is common to insert a comma (or other punctuation) before the coordination in conjoined clauses, but it is less common to insert a comma before the coordinator in conjoined predicates:
> Peter ate the fruit and drank the beer. 
has no comma, whereas in
> Peter ate the fruit, and Peter/he drank the beer. 
the comma is inserted
The commas in
> I send you my very best wishes, and look forward to our next meeting. 
> Margaret is ill, but will soon recover.