What is the simplified form of \(\frac{(n+5)!}{(n+3)!}\)?

Correct answer: \((n+5)(n+4)\)

Expand the larger factorial up to the smaller one: \((n+5)!=(n+5)(n+4)(n+3)!\). The common factor \((n+3)!\) cancels from the numerator and denominator, giving \(\frac{(n+5)!}{(n+3)!}=(n+5)(n+4)\). Option B incorrectly uses \(n+3\) in place of \(n+4\). Exam tip: In factorial division, expand the larger factorial only until the smaller factorial appears, then cancel common factors.