Be prepared that the slabs may not seat together at all again. If a company tries to do it, they may insist on sawcutting the crack which will make it seem even worse.

You're not getting it replaced for the cost of a mudjacking, however, mudjacking to make the crack less conspicuious is a fool's errand.

Take the slab out prep the sub-base and have a new slab poured properly or use pavers, etc that would be your best bet, don't waste money on mud-jacking.

I would definitely bust that up and repour. Good money after bad with mud-jacking as that will be temporary as that is a big crack and I would have to say the ground was not prepared properly.

Same suggestion I give 90% of others cruising the net asking for simple solutions long distance , look for silver bullets in their tool belt and wooden stakes in their tool box.