Question: Expression Manipulation

I have been inspired by videos at this site: (1) Vorperian's Electronic Circuits Courses - YouTube

In these lectures, he shows an example of calculating the resistance of 2 series pairs of resistors in parallel, which is given by

  Eq1

This expression can be simplified, using the parallel operator (sometimes also referred to as the "reciprocal formula" or "harmonic sum") see Parallel (operator) - Wikipedia

`//` := (R1, R2) -> R2*R1/(R1 + R2)

Simplification 
`//`(R1, R2)*`//`(R3, R4)     EQ 2

This is easier to understand EQ2 compared to EQ1
1. Is there a way to display the function as a binary operator as in R1`//`R2 ?

2. Is there a way to add the parallel operator to the simplification procedure?

The videos referenced above go into more complex expressions that I would like to explore, but this seems like the first step.