Re: Combine sqrts in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg122421] Re: Combine sqrts in denominator
• From: Ray Koopman <koopman at sfu.ca>
• Date: Fri, 28 Oct 2011 05:34:05 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j8bcf3\$8s3\$1@smc.vnet.net>

```On Oct 27, 3:40 am, Tom D <tomdick... at att.net> 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

In[1]:= f = 1/Sqrt[-h + Sqrt[h^2 + r^2]] *
1/Sqrt[ h + Sqrt[h^2 + r^2]];

In[2]:= Assuming[{h,r} \[Element] Reals, FullSimplify[f]]

Out[2]= 1/Abs[r]

```

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