What is the value of \(\frac{9!}{8!}+\frac{8!}{7!}-\frac{7!}{6!}\)?

Correct answer: 10

For consecutive factorials, \(\frac{n!}{(n-1)!}=n\), because the common factorial terms in the numerator and denominator cancel. Hence, \(\frac{9!}{8!}=9\), \(\frac{8!}{7!}=8\), and \(\frac{7!}{6!}=7\). Therefore, the value is \(9+8-7=10\). Option 11 would result from incorrectly adding the last term instead of subtracting it. Exam tip: simplify factorial fractions by cancelling common terms first.