Given positive integers x and y such that \(x\neq y\) and \(\frac{1}{x} + \frac{1}{y} = \frac{1}{18}\), what is the smallest possible value for \(x+y\)?
1/x + 1/y = 1/18
18 [ x + y] = xy
18 = xy / [ x + y ]
Let x = 45 and y = 30
18 = 45 * 30 / [ 75 ] = 15 * 3 * 15 * 2 / [ 15 * 5] = 90 / 5
So
x + y = 45 + 30 = 75
Thank you for a nice explanation, CPhill!
+816 
