To repair a split door frame remove the door strip and molding starting at the bottom of the frame and working your way up.
Repair damaged door frame hinge.
Inspect the door hinge and look for where it is loose or hangs off of the door or doorjamb.
Then you can drive the screws into the screw holes on the hinge to secure it.
After time the weight of the door will pull on the hinge and cause the door not to hang straight.
Then measure 6 inches above and below the frame damage and carefully cut the damaged frame away at the marked measurements.
A simple method of using golf tees to fix holes that have been stripped out and are to big so the screws will not tighten up the hinge to the door or jamb.
To relocate the hinge remove the screws from the hinge and slide it up or down a few inches.
You may need to re chisel a pock in the frame so the hinge sits flush.
If you have a centering hinge drill use the hinge as a template and the finish repair will be better than new and last for years.