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Re: rationalize numerator of quotient

• To: mathgroup at smc.vnet.net
• Subject: [mg81182] Re: rationalize numerator of quotient
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 14 Sep 2007 03:49:28 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <fcb3ok$fjj$1@smc.vnet.net> <46E91F86.2080506@gmail.com>
• Reply-to: murray at math.umass.edu

Yes, that does it, thank you.  Of course I was hoping there was some way 
to coerce Mathematica to do it without my explicitly operating upon the
numerator and denominator separately.

I don't know any English-language term for the operation except
something like, "multiply numerator and denominator by the same
quantity".  (Or, as I like to tell my students:  Multiply the fraction
by 1.  Today 1 is .../.... .)

Szabolcs Horv=E1t wrote:
> Murray Eisenberg wrote:
>> I have a quotient such as:
>>
>>    (Sqrt[x] - 2)/(x-4)
>>
>> I want to "rationalize the numerator" by multiplying numerator and
>> denominator each by Sqrt[x] + 2 so as to obtain result:
>>
>>    1/(Sqrt[x]+2)
>>
>> How?
>>
>
> If you mean doing it automatically for any fraction, then I have no
> answer for you ... If you would like to do it manually, then try this:
>
> expansion[frac_, mul_] :=
>  Expand[Numerator[frac] mul]/(Denominator[frac] mul)
>
> (What is the operation of multiplying the numerator and denominator by 
> the same factor called in English?  I used the name "expansion" here, a
> literal translation from my mother tongue, but I am sure it is not
> correct.)
>
> expansion[(Sqrt[x] - 2)/(x-4), Sqrt[x]+2]
>

--
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
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