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Express \(\dfrac{100! - 99! - 98!}{100! + 99! + 98!}\) in lowest terms.

 May 7, 2020
 #1
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Call 98! x. That means that 99! is 99x and 100! is 9900x.

The numerator of the fraction is 9900x-99x-x = 9800x and the denominator of the fraction is 9900x+99x+x = 10000x.

The resulting fraction simplifies to 49/50 which is our answer.

 May 7, 2020

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