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Rewrite equilibrium variables in terms of another variable

I'm wondering how to replace the equilibrium variables in terms of another one. I want the equilibrium to be in terms of a new varible called R = beta*o/(u+y)(u+o) and I can't seem to find the right function that would allow me to do this.

Equilibrium point: S= (u+y)(u+o)/beta*o Want: S = 1/R