Indeed. But remember a PE firm has economies of scale because they own many vet practices. They can negotiate better rates with suppliers than you can, and better payment terms. Maybe they even own some of those suppliers. They can divide their advertising costs by all the practices they own, whereas you can't.
Even if you were willing to be as ruthless as a PE firm, raising your prices and sacking half your staff, and even if you were somehow an expert in financial engineering and business optimization, you still won't make the business as profitable as they can.