Invert and mix.

When you have an instrumental version of a song (from the same stems as the vocal version) this is already one way to get the vocals out without any fancy machine learning. The main tricks besides what you can do in Audacity like that are properly time-aligning the tracks (even if they drift a bit) and compensating for phase issues and compression. I wrote a dirty tool that does that and I've been meaning to turn it into some kind of nicer GUI version.