+0 Given positive integers and such that and , what is the smallest possible value for ?\(Given positive integers $x$ and $y$ such that $x\neq y$ and $\frac{1}{x} + \frac{1}{y} = \frac{1}{15}$, what is the smallest possible value for $x + y$?\)
+129771 1/x + 1/y = 1/15
( x + y) / (xy) = 1/15
(xy) / ( x + y) = 15
xy = 15 ( x + y)
xy =15x + 15y
xy - 15y = 15x
y ( x - 15) = 15x
y = 15x / ( x - 15)
x y
16 240
18 90
20 60
24 40
30 30
40 24
Smallest x + y = 40 + 24 = 64
+129771 True....but i'm assuming that x and y are different integers.....
However....if let them be the same, then your answer is correct
+947
Chris, you were right all along. The problem stipulates x not equal to y.
I had overlooked that in all that run-together text and those dollar signs.
After I realized it, too late to edit, I was relieved that my comment got lost
in the moderation by AI, which btw I maintain is a little short on the "I" part. 
