This randomized phase III trial is studying tretinoin and combination chemotherapy to see how well they work compared to tretinoin, combination chemotherapy, and arsenic trioxide in treating patients with acute promyelocytic leukemia that has not been treated previously. Drugs used in chemotherapy, such as daunorubicin, cytarabine, mercaptopurine, methotrexate, and arsenic trioxide, work in different ways to stop cancer cells from dividing so they stop growing or die. Tretinoin may help leukemia cells develop into normal white blood cells. It is not yet known which regimen is more effective for acute promyelocytic leukemia.