Sorry about the previous post, I was responding via email and the
messages which I though were being viewed together weren't...so I
didn't see your response describing what you wanted. Basically, what
you want is to simplify the insides of the radicals. With the right
assumptions (as Aaron talks about) this will basically allow the
expression to simplify itself. So the following grabs the radicals
(those Pows with exponents having q other than 1) and rebuilds them
after using together on their base and substitutes those expressions
back into the original. The process I use looks like this:

    h[2] >>> a = (1 + x**2/y**2)**(S(1)/2)
    h[2] >>> b = x**2 + y**2
    h[2] >>> f = -1/(a*b) + 3*y/(x**2*a**3*b)
    h[2] >>> p=posify(f)[0] # make all vanilla symbols have positive
assumption
    h[2] >>> pprint(p.subs([(pow, together(pow.base)**pow.exp) for pow
in p.atoms(Po
    w) if pow.exp.q != 1]))
                              4
           y               3*y
    - ------------ + ---------------
               3/2            5/2
      / 2    2\      / 2    2\     2
      \x  + y /      \x  + y /   *x

Is that more what you are looking for?

/c

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