For x and y being integers such that 2<x≤8 and 2<y≤9, we get maximum value of (1/x) − (1/y) when the first term is maximum and the last term is minimum, i.e. x is minimum and y is maximum. This is so because we are dealing with a difference of reciprocals.
Minimum integer value of x is 3
Maximum integer value of y is 9.
Therefore maximum value of (1/x) − (1/y) = (1/3) − (1/9) = (2/9)