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)/(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?
>
> --
> 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
> Amherst, MA 01003-9305
>

```

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