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

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–  Mhenni Benghorbal May 22 '13 at 13:09

$$\frac{7}{x-6}-\frac{3}{x+5}$$