I have a door jamb that is split where the bottom hinge was screwed
into the jamb. My initial thought was to trace an outline of a piece
of replacement wood over the cracked portion, cut it out, and then
slide in the replacement piece.

However, for strength, I'd want to glue it and I'm thinking that
sliding it in would scrape off the glue. Undersizing it would make
the joint weak. There probably isn't room on the backside of the jamb
for a sister board.

There's probably a simple solution...hints?

Thanks