Programming puzzle: Symplifying (simple) fractions containing square roots

[pier4r]

Yup I did this manually (not exactly your solution though, I just wrote the equation, pressed eval, solved), but that uses the power of the CAS I assume (or some well written numeric functions). This because the evaluating function should know how to avoid the root at the denominator. So I went also on the way to use less CAS as possible, saving myself to write a function like FACTORS though.

edit: in other words, let's say that one cannot use functions that are designed to produce exact output with flags -3 and/or -5 cleared.