The state Department of Health on Tuesday approved the merger of Prospect Medical Holdings, a Los-Angeles for-profit company, with Our Lady of Fatima Hospital, in North Providence, and Roger Williams Medical Center, in Providence. The merger of Prospect Medical with CharterCare, which owns the two hospitals, received approval last week from Attorney General Peter F. Kilmartin. The nonprofit hospitals would assume for-profit status. "I hope the implementation of these approvals . . . will strengthen the fiscal condition of these valued hospitals," Michael D. Fine, director of the Department of Health, said in a news release.