Help! End Table is Broken?

Cyanoacrylate(crazy glue). It can be polished. It's what is used to repair broken granite and marble. The back would normally have slots cut in it at the breaks then epoxy put in the slots and stainless steel or brass threaded rod laid in on the backside. However since you may not have access to the diamond blades and grinders to create the slots you can either glue a thin piece of masonite or Formica to the back or laminate fiberglass mesh to the back. If you don't have acces to a polisher use wet sandpaper from an auto store in the thousand grit up range to polish the cyanoacrylate. Scince you haven't done it before sand slowly and check often. Better to start at too fine a grit than at too visited and scratch your table. Glue and clamp it together on a very flat surface to be sure the edges line up. Then apply your choice of liner on the back. If you aren't rodding it. All that being said, check how much it costs for a fabricatour to make you a new one, it's not expensive.