math
posted by Sean on .
Find the solution where x and y are integers to:
1/x + 1/y = 1/14
I can use a computer to get a list of solutions:
7, 14
10, 35
12, 84
13, 182
15, 210
16, 112
18, 63
21, 42
28, 28
but I'm having trouble solving this analytically and coming to a general formula.

1/x + 1/y = 1/14
(x+y)/xy=1/14 Inverse
xy/(x+y)=14
xy=14x+14y
xy14x=14y
x(y14)=14y
xy=14x+14y
xy14y=14x
y(x14)=14x Divide with (x14)
y=14x/(x14)
Solutions:
x14#0
and
y=14x/(x14) x#0 
Do not forget that, since x and y are symmetric, they are interchangeable on your list.
Example: if (13, 182) works, then (182, 13) works as well. 
Go to:
wolframalpha com
When page be open in rectangle type:
1/x + 1/y = 1/14
and click option =
When you see results couple times click option: More Solutions 
bosnian, i already used wolfram alpha to get the solutions I listed. I want to derive the solution analytically.
anon, I believe you just did algebraic rearrangement.