Final answer:
The correct procedure following a maxillary third molar extraction with a fractured tuberosity attached to the soft tissue is to remove the tooth, preserve the tuberosity if stable, and suture the area.
Step-by-step explanation:
When dealing with the extraction of a maxillary third molar where the tuberosity is fractured and both the tooth and tuberosity remain attached to the surrounding soft tissue, the correct procedure is to carefully reflect the mucoperiosteum, remove the tooth, leave the tuberosity in place if it is stable, and then suture the area. This approach prioritizes the preservation of the maxillary bone structure and proper healing.