<s>[INST] How to solve this partial fraction decomposition? Please help me to solve the following partial fraction decomposition:
$$\frac{1-v^2}{v+v^3} = \frac{A}{v}+\frac{Bv+C}{1+v^2}$$
 [/INST] If you play around up- and downstairs you find:
\begin{align*}
\frac{1-v^2}{v + v^3} & = \frac{1-v^2 + v^2 - v^2}{v \, (1+v^2)} \\
& = \frac{1+v^2}{v(1+v^2)} + \frac{-2v^2}{v (1+v^2)}  \\
& = \frac{1}{v} - \frac{2 v}{1+v^2}
\end{align*}
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