Let's begin with recalling the definition of factorial.
The factorial of a positive integer n is the product of the positive integers less than or equal to n.
n!=n*(n-1)*(n-2)*(n-3)* ... * 1
Using this information, we can rewrite the numerator of a given expression.
x!/(x-3)!=x*(x-1)*(x-2)*(x-3)*...*1/(x-3)!
Notice that the expression (x-3)*(x-4)*...*1 is the factorial of (x-3) and we can rewrite it as (x-3)!.
x*(x-1)*(x-2)* (x-3)*(x-4)...*1/(x-3)!
⇕
x*(x-1)*(x-2)* (x-3)!/(x-3)!
Next, we can reduce the fraction by (x-3)! and simplify the expression.
