Using the demolition hammer, chip through the slab, being careful not to further damage the pipe. It is important to expose at least 4 inches of pipe on each side of the damaged section.
Cut out the damaged section of pipe. If the pipe being repaired is cast iron, use a chain type pipe cutter; score the pipe with the cutter, then break out the damaged section using a hammer. If the pipe is ABS, PVC or copper, a reciprocating saw works well. Make the cuts as straight and clean as possible.
Cut a section of new pipe for the patch. The new section should be ¼ inch to ½ inch shorter than the section removed in the previous step.
Slide the flexible couplings onto each end of the new section of pipe, and set the new pipe in place.
Slide the flexible couplings onto the old pipe, so that half of the connector flexible coupling is on the old pipe, and half is on the new pipe. Tighten the connectors in place.
Test the repair. If possible, isolate the repair, and pressure test to 4 pounds per square inch. If a pressure test isn't feasible, run water down the drain to test for leaks.