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Re: Simplify Binomial

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  • Subject: [mg127639] Re: Simplify Binomial
  • From: Andrzej Kozlowski <akozlowski at gmail.com>
  • Date: Thu, 9 Aug 2012 03:53:23 -0400 (EDT)
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On 9 Aug 2012, at 03:36, 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
> 

Your answer is wrong, but anyway FullSimplify won't work here. However:

FunctionExpand[Binomial[m, n + 1]/Binomial[m, n], 
 Element[m | n, Integers] && m > 0 && 
     n > 0 && m > n]

 (m - n)/(n + 1)



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