+194 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.
We have that (a+1/b)(1/b−a)=a2b−1 ≥(−6)25−1=−1915.
Equality occurs when a=−6 and b=5, so the maximum possible value is -191/5.
+194 Cause most of the time, for every question I ask, people post incorrect answers, which doesn't help at all.
