# How to simplify non-commutative expressions

So I want to somehow simplify terms like y(y+1)y^-1. These symbols are not commutative so this is a special case where when you expand the y and y^-1 cancel and you are left with (y+1). How do I do this kind of simplification for much larger and uglier expressions. Specifically, I'm trying to simplify stuff from the map x,y,z to xyx^-1, yzy^-1, yz(y+1) repeated over and over again.