How do I solve this maclaurin series problem?

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Be

$$f(x)=\frac{(6-5x)}{(1-x)(2-x)}$$

how to find the MacLaurin series for $f(x)$?

I can split

$$f(x) \to f(x)= \frac{1}{(1-x)} + \frac{4}{(2-x)}$$

hence

$$f(x)= \sum_{n = 0}^{+\infty} x^n + \sum_{n = 0}^{+\infty} \frac{x^n}{2^{n-1}}$$

is it right answer??

And how do I find $f'''''(0)$?