Extra Element Theorem

I was looking through my files and re-read an old article about the Extra Element Theorem.
This theorem is cool because enables you to analyze a network by removing or adding an element that makes the analysis easier. For example, the input impedance of a bridge circuit with a load on the detection nodes. Without this theorem, I would have done the analysis using nodal or mesh analysis and coming up with a bunch of linear equations. Then I would have to remember Kramer's rule to solve for the variable. The end result is a mess of algebra that gives little insight into the circuit behavior vs. parameters.
The EET allows one to remove the load, analyze three modified bridge circuits (Rin, R looking into the nodes where the element was removed, with the input opened and shorted) and express the result in terms of parallel and series combinations of resistances.

The EET is simple to remember for finding the input Z of any network.
But for finding the transfer functions, it's harder. I couldn't figure it out in 10 minutes.