Given: given: 2 < a < 5, 3 < b < 7 find: a/2b-2b/a

-48/7 < a/2b-2b/a < -11/30

Step-by-step explanation:

a/2b - 2b/a

Get a common denominator of 2ab

a/2b * a/a   - 2b/a *2b/2b

a^2/2ab - 4b^2/2ab

(a^2-4b^2)/2ab

We want to find out the minimum and maximum for the expression

Minimum:

a needs to be the smallest and b needs to be the largest

2^2 -4* 7^2    4-196        -192    -48

= = =

2*2*7            28              28        7

The maximum is when a is the largest and b is the smallest

5^2 - 4*3^2     25-36          -11          

= = =

2*5*3              30             30          

The expression is between

-48/7 < a/2b-2b/a < -11/30

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