Many years ago, my father in law attached two track light rails to one ceiling fixture on a dimmer switch. It lasted until yesterday when I took it down. He had to split the two wires which were both white (having each two sides silver and copper) . The fixture I want to attach has one black , one white and one ground wire . I have put up ceiling fans and lights before . I am probably right about what I think I should do, but I got cold feet. How do I attach the new fixture to the two white split wires , both hanging from the ceiling as two Y's

May not be the correct wiring, But the half of the wire with ridges is the neutral, the smooth is the hot wire.