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If x and y are integers such that $2 < x \leq 8$ and $2 < y \leq 9$, what is the maximum value of $\frac{1}{x} - \frac{1}{y}$?
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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)
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