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# Algebra

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If -5 <= a <= -2 and 2 <= b <= 5, 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 25, 2022

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In order to get the smallest value, you want as big of a negative number x as big of a positive number, so the answer is a super small negative. The way we can do this is by having a = -2, and b = 5.

Plug these values in:

$${({-1 \over 2} + {1\over 5})}* {({1 \over 5} - {-1 \over 2})}$$. This yields $$\color{red} -21/100$$.

Jan 25, 2022