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If $-5\leq a \leq -1$ and $1 \leq b \leq 3$, what is the least possible value of $\displaystyle\left(\frac{1}{a}+\frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) $? Express your answer as a common fraction.

 Jan 14, 2021
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The smallest possible value is 0, when a = -1 and b = 1.

 May 21, 2021

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