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'.
(..) We don't mean to interrupt. We live across the hall. Oh,that's nice. Oh,no,uh,we don't live together. I mean,we live together, but in separate, heterosexual bedrooms. Oh. Okay,well,guess I'm your new neighbor. Penny. Oh. Leonard. Sheldon. - Hi. (..)2007 TvShow: The Big Bang Theory Title: Pilot Season: 1 Episode 1