Question

F(x)=x^3-9x g(x)=x^2-2x-3 What is f(x)/g(x), if x>3

Answer 1

F(x)=x^3-9x
and
g(x)=x^2-2x-3

so you just need to divide f(x) by g(x)

Therefore:

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

and of course you need to factor these two function to see if some factor would cancel another

x^3-9x = x(x^2-9)=x(x-3)(x+3)
and
x^2-2x-3 = (x-3)(x+1)


SO:
$f(x)/g(x) = \frac{(x^3-9x)}{(x^2-2x-3)} = \frac{x(x-3)(x+3) }{(x-3)(x+1)} = \frac{x(x+3)}{x+1}$


Done
:)

I hope you got the idea!

Answer 2

Your answer is 9f/g. Hope it helps