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

Correct answer: \(n^2\)

Using \((n+1)!=(n+1)n!\), the numerator becomes \((n+1)n!-n!=n![(n+1)-1]=n\cdot n!\). Since \(n!=n(n-1)!\), \(\frac{n\cdot n!}{(n-1)!}=n\cdot n=n^2\). Hence, the correct answer is \(n^2\). The expression \(n(n+1)\) would result from incorrectly ignoring the subtraction of \(n!\). Exam tip: In factorial expressions, first rewrite the larger factorial in terms of the smaller one.