The expression you've provided is:

$\frac{N + 2!}{n + 1!}$

This expression can be simplified by first calculating the factorials and then performing the arithmetic operations.

1. Calculate the factorials:

   • $2! = 2 \times 1 = 2$
   • $1! = 1$

2. Substitute these values into the expression:

$\frac{N + 2}{n + 1}$

So, the expression simplifies to:

$\frac{N + 2}{n + 1}$

This is the final simplified form of the expression.

Would you like more details or have any further questions?

Here are 5 related questions:

1. How would you solve the expression if $N = 3$ and $n = 2$?
2. What is the factorial of 5, and how does it apply in expressions like this?
3. How do factorials generally affect the growth of functions?
4. Can you provide an example of a more complex factorial expression?
5. What is the difference between permutations and factorials in combinatorics?

Tip: Factorials grow very quickly, so even small changes in the input can lead to large differences in the result.