simplifying expressions – How do you define a TransformationFunctions to simplify?


I am trying to change the form of some expressions of electrical engineering. A transformation that can help add information is to notice when two resistances are in parallel. The equation for this would be:

$ R_ {parallel} = frac {R_1 R_2} {R_1 + R_2} $

I'm still pretty new to Mathematica, but looking at the Simplify documentation, I think I could do some Transformation function to add to Transformation functions. I looked at the documentation for Transformation functions and the two examples are completely different from the types of equations I've seen that people use in StackExchange.

I have tried to use the following:

pair[e_] : = e /. {R1 R2 / (R1 + R2) -> R Parallel}
Simplify[R1 R2/(R1 + R2), TransformationFunctions -> {Automatic, par}]

and I come back Parallel as I hope, however, if I try

Simplify[R1 R1 R2/(R1 + R2), TransformationFunctions -> {Automatic, par}]

I get (R1 ^ 2 R2) / (R1 + R2) instead. I would have expected to get R1 Rparallel.

I know there are other problems with this, for example, that the transformed name must depend on the input names (for example, R1 and R2 must produce R1R2Paralelo), but I am trying to solve the first problem first.