There is a product called FiberFix that you can use in place of welding. You will have to make sure that what you are reattaching is not riddled with rust and you will have to get some hangers. Head on down to your local parts store with the piece that fell off and they will gladly work with you on getting it back on. FiberFix is pretty damned cool - just wet it and wrap it around the break and it harden like steel.
I used to work in a muffler shop. Exhaust pipes in good condition do not break. They break due to rust and corrosion. You can't weld rusted, corroded metal Back together, it just won't work, You will most likely need more than just a weld.
Go to Midas or somewhere you like and see what a new exhaust will cost you. You can not put a rusted out old one back on.
Just leave it off and everyone will think you have a race car, the girls will want you, and the boys will want to be like you.
This is the car