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

Inclusion Criteria: * Patients must be diagnosed with a platinum-sensitive recurrence of epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer. * The following histologic subtypes are eligible: papillary serous, endometrioid, mucinous, clear cell, adenocarcinomas, transitional, and mixtures of the above. * Patients must have at least one measurable lesion according to RECIST criteria via CT or MRI scan. CT of the chest should be performed if any known disease is present in the chest. Pleural effusions, ascites, bone metastases, CA125 tumor markers, and lesions located in previously radiated areas are not considered measurable. * Patients must have received a platinum-containing regimen at initial diagnosis. * ECOG Performance Status of 0, 1 or 2 * Patients may have received up to 2 prior chemotherapy regimens in the recurrent cancer setting * 18 years of age or older * Life expectancy of greater than 12 weeks * Baseline laboratory values must meet what is outlined in the protocol * Patients must receive vitamin B12 and folic acid prior to starting treatment * Complete recovery from previous chemotherapy or biologic therapy * During the Phase II of the study, patients with significant ascites and/or pleural effusions will undergo consideration of drainage of these areas prior to starting carboplatin and pralatrexate. * Women of childbearing potential must have a negative pregnancy test within 7 days prior to initiating chemotherapy on trial and must agree to practice effective method of birth control during the study and for six months after their last treatment. * Patients must have a normal QTc interval Exclusion Criteria: * Prior pelvic radiotherapy to greater than 25% of bone marrow * Any uncontrolled medical problem that in the opinion of the investigator would preclude safe administration of the study drugs. * Past history of bone marrow transplantation or stem cell support * Patient with known history of CNS metastasis is ineligible unless the patient has had treatment with surgery or radiation therapy, is neurologically stable, and does not require oral or intravenous corticosteroids or anticonvulsants. * A history of prior malignancy except for adequately treated carcinoma in situ of the uterine cervix, incidental stage I endometrial cancer, basal cell or squamous cell skin cancer, or breast cancer (invasive or ductal carcinoma in situ) for which the patient has been disease-free for at least three years. * Routine prophylactic use of G-CSF or GM-CSF within two weeks prior to study entry. * Clinically significant cardiac disease * Uncontrolled hypercalcemia or diabetes mellitus * Any signs of intestinal obstruction that interfere with bowel function and/or nutrition * Grade 2 or greater peripheral neuropathy * Participation in an investigational study within three weeks prior to study entry. * History of anaphylactic shock to prior platinum chemotherapy that would preclude safe administration of study carboplatin. * History of psychiatric disability or other central nervous system disorder as judged by the principal investigator that would be considered significant and that would preclude informed consent, safe administration of study medications and affecting ability to comply with study procedures. * Doses of ibuprofen in excess of 400mg QID. * Interval cytoreductive surgery planned for while subject is on-study. * Recurrence/progression within 6 months of receiving ay platinum regimen * Patients with either pleural effusions or ascites are not eligible for Phase I of the study