+0

# 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(\fr

+1
222
8
+361

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.

Feb 17, 2022

#1
-1

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

Feb 17, 2022
#2
+361
+1

thank you!

Feb 17, 2022
#3
+361
+1

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

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

Feb 17, 2022
#4
+361
+1

i am correct because b=3 and a=-3 then it is 0

Feb 17, 2022
#5
+361
+1

-8/9 if b=3 and a=-1

Feb 17, 2022
#6
+33151
+1

Hmm!  Check the resukt when a = -1 and b = 3.

Feb 17, 2022
#7
+361
+1

ok...

ohhhhhhh it's 8/9

Feb 17, 2022
#8
+361
+1

woops

Feb 17, 2022