Which of the following services can a non-veterinarian not perform?

The correct answer is that a non-veterinarian cannot extract teeth using an elevator. This procedure involves invasive surgical skills and a deep understanding of animal anatomy, as well as the potential for complications that require a veterinarian's expertise. Extracting teeth improperly can lead to significant health issues for the animal, such as infections or prolonged pain.

In contrast, services like administering vaccines, providing basic grooming, and assisting in surgeries can sometimes be performed by trained non-veterinary personnel under the supervision of a licensed veterinarian. Administering vaccines, for instance, can be part of the duties assigned to veterinary technicians and assistants who have received proper training. Basic grooming does not require veterinary expertise and can typically be done by non-veterinarians as a routine care task. Assisting in surgeries, while still requiring supervision, often includes roles that do not involve direct surgical interventions, such as holding instruments or monitoring anesthesia.

Therefore, extracting teeth requires a level of skill and knowledge that is exclusively within the realm of veterinary practice, making it a task that non-veterinarians are not permitted to perform.