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.
The minimum happens when b = 3 and a = -5: (1/(-5) + 1/3)*(1/3 - (-1/5)) = 16/225.
hm..... not sure why but i think it is wrong....
i think there is something smaller..... maybe i am wrong?