what did the tooth look like?
Side/pinion gear teeth are "straight cut", while the ring and pinion teeth are both curved.
It's likely going to be easier, cheaper, and quicker to find another axle, unless it's a side or pinion gear that broke and that's all that's wrong, and you have another donor parts axle in excellent shape laying around.
Typically you get into them and if open, the thrust washers for the pinion gears are shot, which eats into the carrier and the pinion shaft.