<s>[INST] Partial Fraction Decomposition of quadratic factor I'm trying to break up the following equation into partial fractions:
$$\frac{1}{(x^2-1)^2}=\frac{1}{(x+1)^2(x-1)^2}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C}{x+1}+\frac{D}{(x+1)^2}$$
I'm ending up with two equations and four unknowns though:
$$A+C=0 \\ -A + B + C+D = 0$$
(these are the $x$ and constant coefficient variables).
How do I break this up completely?
 [/INST] Alt. hint: $\;\dfrac{1}{x^2-1}=\dfrac{1}{2}\left(\dfrac{1}{x-1}-\dfrac{1}{x+1}\right)\,$, and therefore:
$$
\dfrac{1}{(x^2-1)^2}=\dfrac{1}{4}\left(\dfrac{1}{(x-1)^2}+\dfrac{1}{(x+1)^2}-\dfrac{2}{x^2-1}\right)=\ldots
$$
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