What is the simplified form of \(\frac{(n+2)!}{(n-1)!}\)?

Correct answer: \((n+2)(n+1)n\)

Expanding \((n+2)!\) up to \((n-1)!\) gives \((n+2)!=(n+2)(n+1)n(n-1)!\). Cancelling \((n-1)!\) from the numerator and denominator leaves \((n+2)(n+1)n\). Option B incorrectly omits the factor \(n\). Exam tip: in factorial division, expand the larger factorial only until the smaller factorial appears, then cancel the common factorial term.