SOLUTION: Find all positive integer values of x and y that satisfy the equation 1 over x+x over y+1 over xy=1.

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Question 13903: Find all positive integer values of x and y that satisfy the equation 1 over x+x over y+1 over xy=1.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
First of all,write in math not English and make clear groupings.
Goal,convert the given relation that y is expressed in terms of x.
+1%2Fx+%2B+x+%2Fy+%2B+1%2Fxy = 1.
1%2Fx+%2B+%28x+%2B+1%2Fx%29%2Fy = 1
or +%28x+%2B+1%2Fx%29%2Fy+=+1+-+1%2Fx+
So, +1%2F+y+=+%281-1%2Fx%29%2F%28x+%2B+1%2Fx%29+=+%28x-1%29%2F%28x%5E2%2B1%29

Hence, y+=+%28x%5E2%2B1%29%2F+%28x-1%29+=+%28x+%2B1%29%2B++2%2F%28x-1%29+.
Since, x& y are a positive integer, x-1 must be a divisor of 2.
We have x-1= 1 or 2.
When x = 2, y = 5.
When x = 3, y = 5 (answer:two solutions)
Check the correctness.
Kenny