+0  
 
+1
85
8
avatar+360 

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
avatar
-1

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

 Feb 17, 2022
 #2
avatar+360 
+1

thank you!

 Feb 17, 2022
 #3
avatar+360 
+1

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

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

 Feb 17, 2022
 #4
avatar+360 
+1

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

 Feb 17, 2022
 #5
avatar+360 
+1

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

 Feb 17, 2022
 #6
avatar+32957 
+1

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

 Feb 17, 2022
 #7
avatar+360 
+1

ok...

ohhhhhhh it's 8/9

 Feb 17, 2022
 #8
avatar+360 
+1

woops

 Feb 17, 2022

27 Online Users