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Re: Combine sqrts in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg122438] Re: Combine sqrts in denominator
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 28 Oct 2011 05:37:11 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110271032.GAA08881@smc.vnet.net>

It only simplifies further if you make certain assumptions, e.g.



Assuming[Element[h | r, Reals], FullSimplify[
   1/(Sqrt[Sqrt[h^2 + r^2] - h]*Sqrt[Sqrt[h^2 + r^2] + h])]]

1/Abs[r]


Assuming[Element[h, Reals] && r > 0, 
  FullSimplify[1/(Sqrt[Sqrt[h^2 + r^2] - h]*Sqrt[Sqrt[h^2 + r^2] + h])]]

1/r


Andrzej Kozlowski




On 27 Oct 2011, at 12:32, Tom D wrote:

> I'm doing a calculation that results in terms of the form
> 
> 1/ Sqrt[ -h + Sqrt[h^2 + r^2]] * 1/Sqrt[h + Sqrt[h^2 + r^2]] * (other
> functions)
> 
> One sees that this simplifies to (other functions)/r.
> 
> It would helpful to make Mathematica perform this simplification, but
> I have not been able to get Simplify[] or FullSimplify[] or anything
> else to do it.
> 
> How would I be able to do this?
> 
> Thanks,
> Tom
> 

• References:
  • Combine sqrts in denominator
    • From: Tom D <tomdickens@att.net>