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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.

 May 24, 2019
 #1
avatar+30629 
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"If \(-5\leq a \leq -1\) and \(1 \leq b \leq 3\) what is the least possible value of \(\displaystyle\left(\frac{1}{a}+\frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right)\)?"

 

The image below should help:

 May 24, 2019
 #2
avatar+25481 
+2

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.

 

see: https://web2.0calc.com/questions/help_5056

 

laugh

 May 24, 2019

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