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MathGroup Archive 2007

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Re: rationalize numerator of quotient

  • To: mathgroup at
  • Subject: [mg81160] Re: rationalize numerator of quotient
  • From: Szabolcs Horvát <szhorvat at>
  • Date: Fri, 14 Sep 2007 03:38:02 -0400 (EDT)
  • References: <fcb3ok$fjj$>

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]


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