Question

Simplifying the following:

\[\frac{(n-2)!(n+1)!}{(n!)^2}\]

The way I did it was expanding \((n-2)!\):
\[\frac{(n-2)(n-1)(n)!(n+1)!}{(n!)^2}\]

Then I cancelled out the n! to give:
\[\frac{(n-2)(n-1)(n+1)!}{n!}\]
I tried to continue this by expanding the (n+1)!, then cancelling out the bottom 'n' to give
\[(n-2)(n-1)(n+1)\]

But the correct answer is \[\frac{n+1}{n(n-1)}\]
I'm assuming I made a mistake somewhere or my methodology is not quite right.

Answer 1

do you have an answer key to this?

Answer 2

ohhh idid make a mistake