Answer :

we can see that all the values of our expression are on the range:

9/20 < 1/a + 1/b < 7/12

How to find all the possible values on the given expression?

Here we know that:

3 < a < 4 and 4 < b < 5

And we have the rational expression:

1/a + 1/b

The lower bound of that expression is what we get when we evaluate both values (a and b) in their maximums:

a = 4

b = 5

In that case we get:

1/4 + 1/5 = 5/20 + 4/20 = 9/20

The upper bound is what we get when we evaluate in the minimums:

a = 3

b = 4

1/3 + 1/4 = 4/12 + 3/12 = 7/12

Then we can see that all the values of our expression are on the range:

9/20 < 1/a + 1/b < 7/12

If you want to learn more about rational expressions:

https://brainly.com/question/1851758

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