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g(x) = x/2
It depends on whether fx denotes frequency times variable value or the probability generating function for the variable x.
If it were written in a book of some sort, fx or f(x) is read aloud as "f or x". "f" is a function of some variable, "x". By function it means something happens to x e.g. x2 or 3x+4.
That is the quotient rule and your function is.... f(x) = X^2/x+2 = (x+2)*2x-x^2*1/(x+2)^2 = 2x^2+4x-x^2/(x+2)^2 = x^2 + 4x/(x+2)^2