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Re: Replacement Rule with Sqrt in denominator

I don't want to claim that pattern matching in Mathematica is bugged,
I am certainly not entitled to do so. I was always quite happy to
follow the rules and look at the FullForm in order to create the
correct pattern, until I learned (actually just by following this
thread) that this does not always produce the expected results. So
even though this may not be a bug, pattern matching can be very
confusing sometimes, and, in terms of usability, may seem to be poorly
implemented to some people.
Having said that, could somebody give me a little insight on how
pattern matching "really" works (I'm sure Daniel has done so many
times already, please feel free to refer me to previous posts!):
What set (or class) of expressions does pattern matching exclude from
its "normal" behavior (obviously there is Rational, Complex,
whatnot...)? Why? Are there different such classes? Why does 3/5[[1]]
fail (alternatively: Why does Rational behave differently then List,


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