SOLUTION: Find a positive interger values for a and ab that satisfies the equation 1/a + a/b + 1/ab = 1 Please provide workings Thanks Doug

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Question 465281: Find a positive interger values for a and ab that satisfies the equation 1/a + a/b + 1/ab = 1
Please provide workings
Thanks
Doug
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!


The left side can be condensed into one fraction





We can solve for b in terms of a:





This can be simplified by splitting up the fraction:



Here, we want the quantity 2/(a-1) to be an integer, where a is a positive integer. The only values that work are a = 2, a = 3, and solving for b:

a = 2 --> b = 5
a = 3 --> b = 5

It can be checked that both of these solutions work.