A painful tooth is not necessary to extract. It is enough to remove its nerve and to apply a root filling. Thus it will be still available for chewing. Modern medicine allows for treatment free of pain.
Root end surgery
If the tooth still aches after the root treatment, root end surgery is a good possibility to preserve the function of the tooth. For this purpose, a small cut is placed near its inflammated root end (Apex), which is subsequently being cut off. Thus, the functionality of the tooth is preserved.