<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] if you want to find just $C$ not other two, then look at the behavior of $$ \frac{3x^2 + 17x}{(x+1)(x-2)(x+4)} = \frac{3*(-4)^2+17*(-4)}{(-4+1)(-4-2)(x+4)} +\cdots=-\frac{10/9}{(x-4)}+\cdots$$  therefore $$C = -\frac{10}9. $$
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