A bit more information for you on the frayed edges.
With out seeing it, or knowing how often this occours I could say it could be a couple things.
1.) The nail sheath getting ready to shed, as stated before, though I doubt this is the culprit.
2.) There is nutrients lacking in your cats diet, this can greatly effect their claws and cause for them to be split or frayed like that. It can cause trouble for your cat, they can get caught on things and rip it worse, or take the whole nail out, trap dirt and bacteria inbetween the frayed edges, which increases the risk for infection of the nails.
Are her nails (if they are clear) really discoloured at all, brown/darkish/reddish shades?
I don't remeber exactly what you can add into her diet to help promote proper nail growth but I'm sure your cats doctor could easily tell you.
