Shareholders of the Education Management Corporation today approved the sale of the company to a pair of private-equity firms, Providence Equity Partners and Goldman Sachs Capital Partners. The $3.4-billion deal, which was announced in March (The Chronicle, March 7), is expected to become final on or about June 1, according to a statement issued by the company. Based in Pittsburgh, Education Management owns Argosy University, the Art Institutes, and a number of other colleges specializing in health care, culinary arts, and design. It enrolls about 72,000 students on 72 main campuses in 24 states and two Canadian provinces.