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.
Please help me convert this to proper Latex, also please DO NOT solve all the way, solve halfway and explaining and let me do the rest, thanks :)
