“Should you have a bone graft at the same time as your tooth extraction?”

Treatment is truly up to your doctor ,the operator.

In Most cases it is always best to get bone graft after extraction! however in certain situations is best also not to have bone graft at all! Our body immune system will fill in bone better than artificial bone! It goes case by case! You need to get second opinion of an expert dentist!
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https://celebritydentist.com/

A bone graft is often a good idea if you have already lost a lot of bone or if you plan to have an implant placed at the same location after the extraction

Grafting at the time of extraction is simplest and has a high predictability for regenerating bone within an extraction socket or "hole". The reason is that you will have many tall walls around an extraction socket and those bony walls contain blood vessels that can feed nutrients for healing into the graft site.

If you wait for extraction socket healing with no graft, you'll loose bone. If you have the graft months later, it can be successful but it's harder to re-gain full bone volume. At that point, there is no longer a socket. Any graft material will be packed into a site that's less well surrounded by bone and blood vessels that can provide the kind of nutrition a healing graft requires.