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Re: Simplify problem

• To: mathgroup at smc.vnet.net
• Subject: [mg95841] Re: Simplify problem
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Wed, 28 Jan 2009 06:33:21 -0500 (EST)

On 1/27/09 at 6:58 AM, tidy512 at googlemail.com wrote:

>I am using Simplify / FullSimplify etc. to simplify some equations I
>have, but I am unable to coerce Mathematica into automatically
>giving me the form I require for some of the sub-expressions, e.g.

>I'd like

>1/Sqrt[1 + 1/x]

>to be automatically converted to

>Sqrt[x/(1 + x)]

You can make the desired conversion by using Together. That is

In[21]:= 1/Sqrt[1 + 1/x] // Together

Out[21]= 1/Sqrt[(x+1)/x]

But since

In[22]:= LeafCount[%]

Out[22]= 11

and

In[23]:= 1/Sqrt[1 + 1/x] // LeafCount

Out[23]= 9

Simplify or FullSimplify will clearly not do what you want since
1/Sqrt[1 + 1/x] has a lower LeafCount and therefore simpler by
the definitions of simpler used in these functions.

The real issue is there is no universal definition of simpler
for arbitrary expressions. You could modify
Simplify/FullSimplify to do what you want in this case. But
doing so is likely to have undesirable effects in some other cases.