Find power series representations, centered at $x=0$, for $f(x)$ and the derivative of $f(x)$, where $$f(x)=\dfrac{x^2}{3+6x^3}$$
I am struggling with this question and need help on the steps in order to transition it to a power series.
I believe it will roughly follow the form of $\dfrac 1{1-x}$, but am getting confused. Any help is welcome as I am lost with both the original function and the power series of the derivative $$f'(x)=\dfrac{6x\left(1-x^3\right)}{\left(3+6x^3\right)^2}$$
Hint:
Rewrite as
$$\frac{x^2}3\frac1{1+2x^3}$$ and set $z:=2x^3$.