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'.
(..) And my ax. You carry the fates of us all,little one. If this is indeed the will of the Council... ...then Gondor will see it done. -Frodo's not going anywhere without me. -lt is hardly possible to separate you... ...even when he is summoned to a secret Council and you are not. We're coming too! (..)2001 The Lord of the Rings: The Fellowship of the Ring