Re: Simplify Binomial

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• Subject: [mg127647] Re: Simplify Binomial
• From: Jack L Goldberg 1 <jackgold at umich.edu>
• Date: Fri, 10 Aug 2012 02:44:21 -0400 (EDT)
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```Does anyone know why FullSimplify works in the first case and fails in
the second?  That FunctionExpand works in both is interesting of
course, but IMO this is only part of the answer.

Jack

Quoting Bob Hanlon <hanlonr357 at gmail.com>:

> Binomial[m + 1, n + 1]/Binomial[m, n] //
>  FunctionExpand
>
> (1 + m)/(1 + n)
>
> Binomial[m, n + 1]/Binomial[m, n] //
>  FunctionExpand
>
> (m - n)/(1 + n)
>
>
> Bob Hanlon
>
>
> On Wed, Aug 8, 2012 at 9:36 PM, Themis Matsoukas <tmatsoukas 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
>>
>
>
>
>

```

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