Transformation of equation y=a(100-x)/(a-x) for approximation of separation results plotted as Fuerstenau's upgrading curve for application in other upgrading curves

Equation y= a(100-x)/(a-x), frequently used for approximation of separation results plotted in the Fuerstenau upgrading curve, relating recovery of a selected component of the feed in the concentrate (x = ε) with recovery of another component in the tailing (y = εr), can be transformed into one-fitting parameter equation suitable for other upgrading curves. The mathematical formulas for the so-called Luszczkiewicz, Mayer, Henry, Stepinski, Hall, and Halbich separation upgrading curves were derived and presented.