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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.

 Jul 11, 2023
 #1
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We have that \begin{align*} (a + 1/b)(1/b - a) &= \frac{a^2}{b} - 1 \ &\ge \frac{(-6)^2}{5} - 1 = -\frac{191}{5}. \end{align*}

Equality occurs when a=−6 and b=5, so the maximum possible value is -191/5.

 Jul 11, 2023
 #2
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Wow... the CORRECT answer. So demanding.

 Jul 13, 2023
 #3
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Would you want an incorrect answer to your question???

 Jul 17, 2023
 #4
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Cause most of the time, for every question I ask, people post incorrect answers, which doesn't help at all. 

 Jul 19, 2023

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