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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 :)

 Jul 23, 2021
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You get the maximum vaue when a = -2 and b = 5: (a + 1/b)*(1/b - a) = -99/25

 Jul 23, 2021

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