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Re: Simplify Binomial

• To: mathgroup at smc.vnet.net
• Subject: [mg127620] Re: Simplify Binomial
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Wed, 8 Aug 2012 21:32:59 -0400 (EDT)
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• References: <jvt3qu$lvn$1@smc.vnet.net>

On 8 Aug., 09:17, Themis Matsoukas <tmatsou... at me.com> wrote:
> This works:
>
> FullSimplify[Binomial[m + 1, n + 1]/Binomial[m, n]]
>
> (1 + m)/(1 + n)
>
> but this doesn't:
>
> FullSimplify[Binomial[m, n + 1]/Binomial[m, n]]
>
> Binomial[m, 1 + n]/Binomial[m, n]
>
> How do I get Mathematica to simplify the last result to (m-n)/n?
>
> Thanks
>
>

You will find nobody who can do this ... because it's false.

Use

In[44]:=
FunctionExpand[Binomial[m, 1 + n]/Binomial[m, n]]

Out[44]=
(m - n)/(1 + n)

Regards,
Wolfgang