Question

Find the difference quotient please

Answer 1

Given:

`f(x) = (x)/(x+6)`

Answers:

`f(a) = (a)/(a+6)`

`f(a+h) = (a+h)/(a+h+6)`

`(f(a+h)-f(a))/(h) = (6)/((a+h+6)(a+6))`

Step-by-step explanation:

`f(a+h)-f(a) = ((a+h)(a+6)-a(a+h+6))/((a+h+6)(a+h)) \\ = (a^(2)+6a+ah+6h-(a^(2)+ah+6a))/((a+h+6)(a+6)) \\= (6h)/((a+h+6)(a+6))`

`(f(a+h)-f(a))/(h) = (6)/((a+h+6)(a+6))`