Broken rear axle. Why does it happen and is it worth trying to repair?
Most of times the axle is broken when not accurately jumping with bike (the same is with obstacles on road like holes and speed bumps). Wheels with freewheel are more exposed to this because their bearings (i.e. the place where wheel touching the axle) far from the place where the bike touch the wheel, therefor it have more moment to brake the axle.
To the question about worth repair. The only available repair of this - is to put a new axle, that means it will be like a new wheel (if you do not have other problems in your wheel). If you going to replace the axle, examine the bearings cup if it have any deformation. If it have, in most cases the wheel must be replaces. Examine also the cones.