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Re: Combine sqrts in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg122417] Re: Combine sqrts in denominator
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Fri, 28 Oct 2011 05:33:21 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j8bcf3$8s3$1@smc.vnet.net>

On 2011.10.27. 12:40, 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?
>

Tell Mathematica that h and r are positive reals:

Simplify[1/(Sqrt[-h + Sqrt[h^2 + r^2]]
   Sqrt[h + Sqrt[h^2 + r^2]]), h > 0 && r > 0]

In Mathematica, saying that they're positive implies that they're real.