<s>[INST] Un-Simplifying a fraction, i.e. computing partial fraction decomposition $\frac{3x^2+17x}{x^3+3x^2+-6x-8}$
I need to find the value of C in the form of 
$\frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{x+4}$
which is based on the fraction give at the top.
I can get so far to do the following:
$A(x^2+2x-8) + B(x^2+5x+4) + C(x^2-x-2) = 3x^2+17x$
No clue on my next step or even if this is the right step.
 [/INST] $$
\begin{align*}
\left(A+B+C\right) x^2 &= 3x^2 \\
\left(2A + 5B -C\right)x &= 17x \\
-8A + 4B - 2C &= 0
\end{align*}
$$  
Dividing the first equation by $x^2$ and the second by $x$ will get you a linear system of equations.
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