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Re: rationalize numerator of quotient
 To: mathgroup at smc.vnet.net
 Subject: [mg81167] Re: rationalize numerator of quotient
 From: "David Park" <djmpark at comcast.net>
 Date: Fri, 14 Sep 2007 03:41:41 0400 (EDT)
 References: <fcb3ok$fjj$1@smc.vnet.net>
The problem is to avoid immediate cancelation of the two factors. There are
probably a number of ways. Here are two.
MultiplyByOne::usage =
"MultiplyByOne[onefactor][expr] will multiply by onefactor and \
expand both the numerator and denominator of expr before \
simplifying.";
MultiplyByOne[onefactor_][expr_] :=
Simplify[Expand[one Numerator[expr]]/Expand[one Denominator[expr]]]
(Sqrt[x]  2)/(x  4) // MultiplyByOne[Sqrt[x] + 2]
1/(2 + Sqrt[x])
MultiplyByOne::usage =
"MultiplyByOne[onefactor][expr] will first multiply expr by \
onefactor and expand, then divide by onefactor and simplidy.";
MultiplyByOne[onefactor_][expr_] :=
With[{work = Expand[onefactor expr]},
Simplify[work/onefactor]]
(Sqrt[x]  2)/(x  4) // MultiplyByOne[Sqrt[x] + 2]
1/(2 + Sqrt[x])

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"Murray Eisenberg" <murray at math.umass.edu> wrote in message
news:fcb3ok$fjj$1 at smc.vnet.net...
>I have a quotient such as:
>
> (Sqrt[x]  2)/(x4)
>
> 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?
>
> 
> Murray Eisenberg murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower phone 413 5491020 (H)
> University of Massachusetts 413 5452859 (W)
> 710 North Pleasant Street fax 413 5451801
> Amherst, MA 010039305
>
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