Carboplatin/Pralatrexate in Recurrent Platinum-Sensitive Ovarian, Fallopian or Primary Peritoneal Cancer

* Since we are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects, not everyone who participates will receive the same dose of the study drug. * Each study cycle will last 28 days. On Day 1, participants will receive carboplatin intravenously. On Days 1 and 15 of each cycle they will receive pralatrexate intravenously. Participants will also be asked to take folic acid orally on a daily basis starting 7 days before the first dose of pralatrexate and continuing until 30 days after the last dose of pralatrexate. They will also receive a vitamin B12 injection no more than 10 weeks prior to the first dose of pralatrexate and every 8-10 weeks after the first dose of pralatrexate. * Participants will come to the clinic on Day 1 and 15 of each cycle and have the following tests/procedures performed: Medical history; Vital signs; Blood tests, assessment of the tumor (every two cycles) and an EKG (before the start of cycle 2). * In addition, during Cycle 1, participants will come to the clinic weekly for blood tests. * Pharmacokinetic (PK) blood samples (to monitor how the body absorbs and breaks down the study drug) will be done at the following time points during Cycle 1: Day 1-3 and Day 15-17. * Participants will be asked to take the study drugs for up to 6 cycles. They may continue beyond 6 cycles as long as there is evidence that the tumor is not growing and they are not experiencing any unacceptable side effects.