we can see that all the values of our expression are on the range:
9/20 < 1/a + 1/b < 7/12
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
#SPJ1