Question

(The question is in exact wording to the original problem)

Suppose 3<a<4 and 4<b<5. Find all possible values of each expression.

(b/3a)-(a/3b)

What I got correct so far:
0<(b/3a)-(a/3b)< (What I need to complete this problem)

Please help and thank you to the people that do.

Answer 1

for x-y to be greatest, x needs to be greatest and y needs to be least
b/3a is greatest when bis big and a is small: 5/9
a/3b is least when a is small and b is big: 3/15 = 1/3
so b/3a - a/3b is greatest at 5/9 - 1/3 = 2/9

Now find when b/3a - a/3b is least, and then you have your range of values.