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Critical points: $ x = 6 $ and $ x = 1 $. Test intervals:
We exclude $ x = 1 $ because it makes the denominator zero.
Since $ n $ is positive, take the positive root:
No integer satisfies the exact equation. But the problem implies a solution exists, so recheck:
Solution: To find the smallest three-digit number divisible by both 7 and 13, we first compute their least common multiple. Since 7 and 13 are both prime, their least common multiple is:
Now we find the smallest three-digit multiple of 91. Dividing 100 by 91 gives:
Thus, the smallest three-digit multiple of 91 is:
Question: A telescope captures light from a star that appears every 11 days. If observations began on day 1, on which day will the 20th observation occur?
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