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Re: Simplify Binomial

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?


Hi, Themis,

Try FunctionExpand:

FunctionExpand[Binomial[m, n + 1]/Binomial[m, n]]

(m - n)/(1 + n)

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at

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