<s>[INST] Taylor Series $(x+2)/(2-3x)$ at $x=2$ How can I find Taylor series for  $$\frac{(x+2)}{(2-3x)}$$ at $x=2$? 
 [/INST] Hints:
$$\frac{x+2}{2-3x}=(x+2)\;\frac13\;\frac1{2-x-\frac43}=-\frac{x+2}3\;\frac34\;\frac1{1+\frac{3(x-2)}4}=$$
$$=-\frac{x+2}4\left(1-\frac{3(x-2)}4+\frac{9(x-2)^2}{16}-\ldots\right)$$
Well, now find the general expression for the above and for what values of $\;x\;$ it is valid.
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