Can someone please help on a math problem?

Question

For the functions f(x)=x^2-9 and g(x)=x-3
Find and simplify. (f-g/5g)(x)

I can't find an example anywhere in my math book to help me solve this problem. Can someone please help? Thank you!

Answer 1

Given functions are f(x) = x^2 - 9 and g(x) = x - 3

 (f - g/5g)(x) = (x^2 - 9 - (x - 3)) / 5(x - 3)

                     = (x^2 - 9 - x +3) / 5(x - 3)

                     = (x^2 - x - 6) / 5(x - 3)

                     = (x^2 +2x -3x - 6) / 5(x - 3)

                     = [x(x + 2) -3(x + 2)] / 5(x - 3)

                     = [ (x - 3) (x + 2) ] / 5(x - 3)

                     = (x + 2) / 5

Therefore  (f - g/5g)(x) = (x + 2) / 5