<s>[INST] Partial Fraction Decomposition of $\frac{x^4+2}{x^5+6x^3}$ I tried answering the following question but I'm getting it wrong for some reason. I would appreciate any help.
$$\frac{x^4+2}{x^5+6x^3}$$
My answer:
$$\frac{A}{x}+\frac{Bx+C}{x^2}+\frac{Dx+E}{x^3}+\frac{Fx+G}{x^2+6}$$
What am I doing wrong?
 [/INST] The typical way to deal with $(x+b)^n$ in the denominator is to have the terms
$$ \frac{A_1}{x+b} + \frac{A_2}{(x+b)^2} + \dots + \frac{A_n}{(x+b)^n}$$
Note that $A_2$, $A_3$ etc are constant terms.
In your case, try expressing it in the form
$$\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{Dx+E}{x^2+6}$$
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