Factorial mathematics: ACT Math Practice Question

Try this ACT math practice question on dealing with algebraic manipulation of factorial expressions..

Which of the following expressions is equivalent to
$$\left[1 \quad – \quad\dfrac{(n!)^2}{(n+1)!(n-1)!}\right]$$ where $n>2$ and $n! = n(n-1)(n-2)\cdots 3 \cdot 2 \cdot 1$ ?

1. $\quad \dfrac{n-2}{n+1}$
2. $\quad \dfrac{1}{n+1}$
3. $\quad \dfrac{2}{n^2-1}$
4. $\quad \dfrac{1}{n-1}$
5. $\quad \dfrac{n}{n+1}$

Choice B