If it's a fungal infection then you need to treat it. You also need to be careful to not spread the infection to other nails.
If it's not a fungal infection, it could be a mineral deficiency. Again, it needs to be treated. Also, you are at risk of fungal or bacterial infection through the split.
What I have done and recommend you do - first, treat the nail. Talk to a pharmacist or see a doctor about the split and what it means. A doctor could do a scraping to test for fungal infection.
Next - get some fibreglass nail wraps. You can buy these fairly cheaply. I've actually used other things instead of these such as a scrap of 'cloth' torn off a baby wipe, but the fibreglass wraps are much thinner and stronger. They also disappear when you put them on properly. The baby wipe option - I had to keep the nail covered with coloured nail polish and it also kept snapping off.
Now, to apply - carefully trim the fibreglass (on the backing paper) to fit. I tend to not cover the whole nail if it's just a side split I'm trying to repair, but I'm experienced at this. In your case, I think aim to almost cover the whole nail. Don't go right to the edge, you risk accidentally lifting the wrap in daily use.
Next - scuff up your nail surface a little, using an emery board. You don't apply this stuff to buffed smooth nails. Remove any nail polish. Make sure your nails are clean, dry and not greasy. If you've applied a slightly oily treatment to the nail split, make sure that either side of the split is clean, dry and non-oily (I'm assuming the split is fairly central?)
So after you've done all this, you remove the fibreglass wrap from the backing paper and stick the wrap onto your nail. It could slide around a bit. Or maybe mine do that because they're so old that the adhesive doesn't really work any more. My wraps are over ten years old. One packet lasts ages even though I've also used them on difficult child 1, plus husband uses them too.
Stick the wrap down as best as you can, smoothing it out gently. The fibreglass can fray easily, try to not let it fray too much. Trim any long threads that fray off.
Now - get your clear nail polish or your Sally Hansen's nail mender polish or hard-as-nails clear nailpolish (not the nail hardener that isn't a polish - you need a nail polish-type product here) and gently paint it over the fibreglass wrap. If the wrap moves out of place, use a toothpick or the edge of another fingernail or even the tip of your nail scissors to slide it back into place. Then let it dry. Thoroughly. This is important enough to do nothing while it dries, you need this job to be good. You can use the time to coat the rest of your nails with clear polish if you want, so they all look the same. But you probably won't want to bother. I tend not to.
Once the polish is dry, trim off any frayed bits you missed and gently file the edges with an emery board. Then give a lihgt coat again, to cover any exposed fibreglass edges.
Now, nail polish wears. And where it wears fastest, is on the edge of the nail. So the first chips will appear there, the more you work with your hands. So each day you need to make sure that at least the tip of the nail is protected. Maybe after doing this you can leave it until the second day, but you will need to lightly re-coat every couple of days at least, just with the nail polish.
If the whole thing lifts off and you can catch it, then you can stick it all back down again as follows - coat your nail with clear polish, then stick the old wrap-polish ensemble back down. You're using the nail polish as glue, here. Some of it will penetrate into the wrap's underside to help bond. Hold the wrap onto your finger for a few minutes after you put it on, then leave off doing anything with that hand for an hour or so, to let the bond harden.
Your aim is to keep the split in the fingernail covered and protected while the nail grows out. You will need to replace the wrap every so often, to keep it covered properly and to avoid that ridge effect.
If you want to cut your nails while you've got a wrap on, that's OK. But the cut edge will need to be sealed with a lick of nail polish.
You can't remove the nail polish with remover, while you're wearing a wrap. so if you choose to use fluorescent day-glo orange nail polish and decide you prefer baby blue, you need to start over completely. That's why it's best to use clear. Whatever colour you use, that's your signature colour for the season!
I hope this helps.
husband gets split nails often, and lately he's been using the wraps more than I do. It's good for toenails, too.
Marg