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Your cuticles are the pieces of skin that you can see over the top of your nail near the knuckle. It's important to have healthy cuticles to avoid hangnails. That means not letting the skin dry out too much. The best way to do this is to regularly apply cuticle oil to moisturise them. You can use a regular hand cream, or moisturiser designed specifically for the cuticles. Applying cuticle oil once a day before bed can make a big different to your cuticle health. As well as caring for your cuticles, moisturising the skin around the sides of your nails will help prevent hangnails. Applying a basic hand cream to your fingers, focussing on the area around the nail once or twice a day will help you have healthier, and less dry skin in this sensitive area. A lotion or cream with vitamin E can hydrate and soothe nicks and cuts. Petroleum jelly is a great moisturiser that is easy to get hold off. If you have painted your nails and you find that some of the polish has made it's way onto the skin around your nails, be sure to remove it quickly. Nail polish will dry out your skin, so wash it off carefully without picking at it. This applies to base coat as well as top coat. Acetone-based nail polish remover will also dry out the skin around the nails.
Moisturise your cuticles. Moisturise the skin around your nails. Clean up stray nail polish.