Please help! My nail tips keep slitting.

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Finally, after years of being a compulsive nail biter, I've gone cold turkey. And, now my nails are almost to the tips of my fingers. Not bad for two weeks work. I've been taking better vitamins, so I think that helps. But, the problem is that my nail tips get so ragged after bath time and doing dishes, that they tear. I've had this problem every time I try to grow my nails and usually end up so frustrated that I bite them off. Can you give me some tips to make my nails stronger? My nails aren't brittle, just very soft. Would appreciate your help!