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If $-6\leq a \leq -2$ and $3 \leq b \leq 5$, what is the greatest possible value of $\frac{a + 1/b}{a - 1/b}$? Express your answer as a common fraction.

 Aug 30, 2023
 #1
avatar+4 
+1

I need answeer too 👀👀👀

 Aug 30, 2023
edited by alexwrinner  Aug 30, 2023
 #3
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Oh, you homework cheaters are in the same class?

Guest Aug 30, 2023
edited by Guest  Aug 30, 2023
 #2
avatar+125627 
+1

\(-6\leq a \leq -2 and 3 \leq b \leq 5\)

 

Note that   [ a + 1/b ] /  [ a - 1/b]  =    [ (a + b) / b ]   [ (a - b) / b ] =  [ a + b  ]  /  [a - b ]

 

This will be maximimzed when    a = -6 and b = 3 

 

So [ a + b ] / [ a - b ]  =  [-6 + 3 ] / [ -6 - 3]  =   -3 / -9  =  1/3

 

 

cool cool cool

 Aug 30, 2023

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