Find f(x) and g(x) such that h(x)=(fog)(x)

Question

h(x)=x^2-9 / x^2+9

Answer 1

one way would be
g(x) = x^2+9
f(x) = (x-18)/x
so, (fog)(x) = f(g) = (g-18)/g = (x^2-9)/(x^2+9)

There are other ways, too, of course.