What is the simplified form of \(\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}}\)?

Correct answer: \((n+4)(n+3)\)

The \(n!\) factors cancel in the given complex fraction:
\(\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}}=\frac{(n+4)!}{(n+2)!}\).
Since \((n+4)!=(n+4)(n+3)(n+2)!\), the factor \((n+2)!\) cancels, leaving \((n+4)(n+3)\). Option C does not result from cancelling the factorials correctly. Exam tip: expand the larger factorial only up to the smaller factorial before cancelling common factors.