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s3.5.2

a! ± b! / c!

1,000 questions

These problems involve simplifying fractions with factorials. The key is usually to factor out the smallest factorial in the expression.

For example, 8!+6!7!=8×7!+6!7!=8+6!7!=8+17=817\frac{8! + 6!}{7!} = \frac{8 \times 7! + 6!}{7!} = 8 + \frac{6!}{7!} = 8 + \frac{1}{7} = 8\frac{1}{7}.

Another example: 3!+4!5!3!=3!(1+4(5×4))3!=1+420=15\frac{3! + 4! - 5!}{3!} = \frac{3!(1 + 4 - (5 \times 4))}{3!} = 1 + 4 - 20 = -15.

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