What is the numerator of the simplified sum? StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction

4x + 6

Step-by-step explanation:

Given

+

Before we can add the fractions we require them to have a common denominator.

Factor the denominator of the first fraction

+

Multiply the numerator / denominator of the second fraction by (x + 2)

= + ← fractions now have a common denominator

Add the numerators leaving the denominators

=

=

= ← simplified sum with numerator 4x + 6

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).