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'.
(..) Now, it concludes that... ...the most logical delivery system for the terrorist to use... ...would be an airborne attack. A separate report has been filed... ...suggesting a train, despite the fact that the tunnels surrounding Parliament... ...have been sealed shut. Chief Inspector Finch. (..)2005 V for Vendetta