       Re: Combine sqrts in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg122437] Re: Combine sqrts in denominator
• From: "David Park" <djmpark at comcast.net>
• Date: Fri, 28 Oct 2011 05:37:00 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <15715639.102984.1319708960115.JavaMail.root@m06>

```expr = 1/Sqrt[-h + Sqrt[h^2 + r^2]]*1/Sqrt[h + Sqrt[h^2 + r^2]];

Simplify[expr, h > 0 && r > 0]
1/r

Also:

Simplify[expr, h \[Element] Reals && r > 0]
1/r

Simplify[expr, {h, r} \[Element] Reals]
1/Abs[r]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Tom D [mailto:tomdickens at att.net]

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

```

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