How do I check using MATLAB if a symbolic expression evaluates to zero?

I want to verify using MATLAB that the expression:

nchoosek(n+1,k)*2^(-n-1) - nchoosek(n,k)*2^(-n) + nchoosek(n,k)*2^(-n-1) + nchoosek(n,k-1)*2^(-n-1)

is identically zero.

I have tried using 'simple' and 'simplify' but MATLAB doesn't boil the expression down to zero.

Please help.

Thanks.

[José-Luis]

How do you do that? Could you post a sample of your code?