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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

 Jun 30, 2021
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$\frac{j+k}{jk} = \frac{2}{3}$

$3j + 3k = 2jk$

$3j - 2jk + 3k = 0.$

 

Here is the graph: https://www.desmos.com/calculator/u6uyo6fqj3

Consider asymptotes and reflections. LMK if you have any more questions.

 Jun 30, 2021

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