Ok this is what I have discovered after fifty years of nails breaking down low at the sides. Buy some nail glue on ebay. About £3.00. Break up a tea bag (and throw away the tea inside!) Cut a tiny bit off the tea bag, just big enough to cover the break. Put a tiny dob of glue over the broken nail (put the glue carefully on a cocktail stick/wooden toothpick first otherwise you will get glue under all your nails and then they will all stick together - nail glue is stronger than superglue). So tiny dob on the break. Put a small piece of teabag over the glue. Just large enough to cover the break. Push it down with the toothpick. another small dob of glue. Let it dry. Keep a cloth handy to wipe up any spillages, take care of the glue, as I say you can stick all your fingers together if you aren't careful. Undercoat, varnish, topcoat. When the glue is dry it is so strong with the teabag on it, otherwise just glue on the nail doesn't last long. Sorry that was so long winded, but it does work, and always use acetone free varnish remove afterwards.