If \(-5\leq a \leq -1\)and \(-5\leq a \leq -1\), 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.

XxmathguyxX Feb 17, 2022

#1**-1 **

The minimum happens when b = 3 and a = -5: (1/(-5) + 1/3)*(1/3 - (-1/5)) = 16/225.

Guest Feb 17, 2022

#3**+1 **

hm..... not sure why but i think it is wrong....

i think there is something smaller..... maybe i am wrong?

XxmathguyxX Feb 17, 2022