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Re: Combine sqrts in denominator

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122416] Re: Combine sqrts in denominator
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 28 Oct 2011 05:33:11 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201110271032.GAA08881@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Forget about the (otherfunctions) factor and look just at:

   expr = 1/(Sqrt[-h + Sqrt[h^2 + r^2]]*Sqrt[h + Sqrt[h^2 + r^2]])

This does _not_ always equal 1/r. For example:

   expr /. {h -> I, r -> -2} // Simplify

gives 1/2 rather than 1/(-2) as output.

Perhaps you want:

   expr // Simplify[#, h >= 0 && r >= 0] &


On 10/27/11 6:32 AM, 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
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305



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