Find the Maclaurin series for function $f(x)$ and determine its interval of convergence.

Question

$$f(x) = \frac{3}{1+x-2x^2}$$ I have to evaluate $f^{(8)}(0)$ and find its interval of convergence. The problem is I don't know how to find it since counting derivatives ($f''(x)$, $f'''(x)$, ...) is tedious. Is there any way to do it in faster and more efficient way?