Simplify the following factorial expression. \[ \frac{(9 n) !}{(9 n+1) !} \] $\frac{(9 n) !}{(9 n+1) !}=$ (Simplify your answer.)

Step 1 ：The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. The factorial function can be defined by the product n! = n*(n-1)!

Step 2 ：In the given expression, the denominator is the factorial of (9n+1), which can be rewritten as (9n+1)*9n!. This means that the expression can be simplified by cancelling out the common factor of 9n! in the numerator and denominator.

Step 3 ：Final Answer: The simplified form of the given factorial expression is \(\boxed{\frac{1}{9n+1}}\)