You need to understand where your fingernails are formed and why it's so important to not damage that area. At the base of your fingernail and behind the cuticle, under the skin is the matrix where your fingernail is actually formed. It continues to form nail, pushing out the old.
From the time your new nail is visible beyond the cuticle, it is considered to be dead matter. What that means is, past the actual bed of your nail, the fingernail is continuously losing its oils. That's why they will eventually break. To keep nicely formed nails, be careful not to damage the matrix. A bruise on the matrix, will show up as a black spot on the nail, as it grows out.
The biggest mistake most folks make, is in removing too much of the cuticle. That cuticle is there for a purpose and constantly trying to get rid of it, weakens your fingernail. If you tend to your own fingernails at home, remember to clean off the dead cuticle that has adhered to your fingernail, while leaving to padding of good cuticle in place. Your fingernail needs that.
The best way to battle brittle, splitting fingernails, is by taking care of the cuticle. If you live in a very arid area, I'd suggest applying a good fingernail moisturizer at night. If you are having problems with brittle nails, splitting off in layers and your have long fingernails, you might take note of how many times you bang the tip of your nail into things. If they are so long, that you can't keep from jamming the end of your finger, you need to shorten them for the sake of the matrix. Jamming the tip of your fingernail, bruises the matrix and just adds to the brittle problem.
When removing nail polish, take note if your fingernail is truly dry. If so, change brands of fingernail polish until you find one that does not dry out your nails. It's best to go without polish for a day or two, between manicures, to give the nail bed a chance to breathe.
If you ever happen to notice the bed of your nails, seeming to have a slight ache, it's a sign you're wearing the wrong brand for you. It seems like such a simple thing but taking care of your cuticle and matrix, could very well cure that splitting and layering off of the fingernail.