Walls and Ceilings - Cracked wallboard, how to repair?

I have a piece of sheetrock that has apparently cracke over a stud due to the settling of my chimney. When in escrow, the inspectors determined that the settling isn't unsafe and doesn't need to be repaired. Unfortunately, after removing an installed bookcase, I see a large crack in the wall.

I'd like to repair it. I wanted to slightly widen the crack with a knife and fill it in with joint compound. Then when the first coat was dry, tape the crack over and then apply a few more coats to smooth out the entire wall(about 8' long and goes straight to the ceiling), and finally apply some texture.

Is this an acceptable way to repair the wall?

Thanks,

Sam

Make your cut describe a "V", apply hot mud, apply web tape, smooth, coat again and feather out with an 8" knife.
Finish coat, sand and paint.

WHen I said "slightly widen" I meant cutting a 'V' groove in it. THat is what I'll do then.

Thanks again.

Sam