Finding power series for $f(x) = \frac{4x+53}{x^2-x-30}$ 
Given $f(x) = \dfrac{4x+53}{x^2-x-30}$, display it as a power series and find the radius of convergence. then calculate $f^{(20)}(0)$

So what I did was look at the Taylor Series Formula:
$$f(x) = \sum_{n=0}^{\infty} {\frac{f^{n}(0)}{n!} x^n } $$

$f(0) = \dfrac{53}{-30}$ and $f'(0) = \dfrac{-67}{(-30)^2}$.

But after that it only gets harder and harder to derive, thus making it harder to see a general form of the $n$th derivative.
Would be happy if someone gave me a direction.
Thank you

Hint: Use partial fractions, and write it as the sum of geometric series.  Result:
$$\frac{7}{x-6}-\frac{3}{x+5}$$
