He tries to keep his private life and public life 'separate' (from each other). = He tries to keep his private life 'separate' from his public life.
('US') He fell and 'separated' [='dislocated'] his shoulder. [=caused the bone in his shoulder to move out of its proper position]
The competition has been easy to this point, but now it gets tough and we'll really begin to 'separate the men from the boys'.
(..) It was a success. Ava demonstrated true Al and you were fundamental to that. So if you can just, for a second, separate... - Power cut. - Backup power activated. Well, I guess it's . Ava's gonna be wondering where you are. (..)2014 Ex Machina