If \(-6\leq a \leq -2\) and \(3 \leq b \leq 5\), what is the greatest possible value of \(\displaystyle\left(a+\frac{1}{b}\right)\left(\frac{1}{b}-a\right) \)? Express your answer as a common fraction.
Simplifying the given expression we get
1/ b^2 - a^2
The first term will be greatest when b = 3 and the second term will be least when a = -2
So....the max value is
1/(3)^2 - (-2)^2 = 1/9 - 4 = -35/9
