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

Correct answer: \(n+2\)

Using \((n+1)!=(n+1)n!\), the numerator becomes \((n+1)n!+n!\). Taking \(n!\) common gives \((n+2)n!\). On dividing by \(n!\), the result is \(n+2\). The expression \(n+1\) accounts only for \((n+1)!/n!\); the additional term \(n!/n!=1\) must also be included. Exam tip: In factorial expressions, first rewrite the larger factorial as a multiple of the smaller one.