Given:
[tex]f(x) = \frac{x}{x+6} [/tex]
Answers:
[tex]f(a) = \frac{a}{a+6} [/tex]
[tex]f(a+h) = \frac{a+h}{a+h+6} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
Explanation:
[tex]f(a+h)-f(a) = \frac{(a+h)(a+6)-a(a+h+6)}{(a+h+6)(a+h)} \\ = \frac{a^{2}+6a+ah+6h-(a^{2}+ah+6a)}{(a+h+6)(a+6)} \\= \frac{6h}{(a+h+6)(a+6)} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
