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\(\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = r*\frac{1}{3}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})\) - if you divide LHS by last factor on RHS, I think you get 1.

So in highlighted part, \(r*\frac{1}{3} =0\), I think RHS should be 1, not 0. Otherwise you'll get

\(r*\frac{1}{3} * 3 =0 * 3\)

\(r = 0\)
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To solve this question, we need to recognize that there's a 1/3 + 1/4 + 1/5 + 1/6 "hiding" in 1/9 + 1/12 + 1/15 + 1/18 We can reveal this "secret" by factoring 1/3 out of 1/9 + 1/12 + 1/15 + 1/18 We get: 1/9 + 1/12 + 1/15 + 1/18 = (1/3)(1/3 + 1/4 + 1/5 + 1/6)

So..... Given: 1/3 + 1/4 + 1/5 + 1/6 = r(1/9 + 1/12 + 1/15 + 1/18) Factor right side to get: 1/3 + 1/4 + 1/5 + 1/6 = (r)(1/3)(1/3 + 1/4 + 1/5 + 1/6) Divide (1/3 + 1/4 + 1/5 + 1/6) from both sides to get: 1 = (r)(1/3) Multiply both sides by 3 to get: 3 = r Answer:

To solve this question, we need to recognize that there's a 1/3 + 1/4 + 1/5 + 1/6 "hiding" in 1/9 + 1/12 + 1/15 + 1/18 We can reveal this "secret" by factoring 1/3 out of 1/9 + 1/12 + 1/15 + 1/18 We get: 1/9 + 1/12 + 1/15 + 1/18 = (1/3)(1/3 + 1/4 + 1/5 + 1/6)

So..... Given: 1/3 + 1/4 + 1/5 + 1/6 = r(1/9 + 1/12 + 1/15 + 1/18) Factor right side to get: 1/3 + 1/4 + 1/5 + 1/6 = (r)(1/3)(1/3 + 1/4 + 1/5 + 1/6) Divide (1/3 + 1/4 + 1/5 + 1/6) from both sides to get: 1 = (r)(1/3) Multiply both sides by 3 to get: 3 = r Answer:

I kept looking what is that I cannot see. I could not spot it. I solved it manually in 2 minutes and got the right answer and then I was able to see. Hahaha!
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