simplification of binomials



Hi, is there some way to simplify stuff like this?

  binomial((t + 1)*(n + 1), n + 1)/binomial((t + 1)*n, n)

On a related note, I couldn't figure out a way to get (n + 1)!/n! to
yield (n + 1).
I'm probably overlooking something obvious.

Thanks for any info.

Robert Dodier