Use scissors to cut away any frayed ends of carpet and make it even. Leave the rest of the carpet intact -- do not cut into it or more frays may appear.
Ensure that your binding and thread are the same color as the carpet and/or its original binding.
Cut a strip of new binding to fit over the carpet. It should overlap the fray.
Whipstitch the new binding over the carpet with the needle and thread from the right to left.
Put on rubber gloves and then wet a rag under plain tap water. Use this rag to blot up any excess glue as you bind the carpet back together. Squeeze carpet seam sealer onto the damaged spot where the fray appeared. Immediately wipe up any excess sealer with the wet rag.
Press the carpet seam into the glued area. Let the carpet seam glue to dry over a 24-hour time period or as long as suggested by the adhesive manufacturer.
Inspect the bind/seam after 24 hours and then in 48 hours to ensure it does not split apart again. Should any fraying begin to reappear, repeat these instructions.