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Mathematics
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Other answers:

did you try partial fractios?
**fractions
Yes partial fraction is the way.
hw to make the work less tedous seems a lot of wrk is needed
Oo .. I found and error.
?
wolfram is the smartest http://www.wolframalpha.com/input/?i=partial+fractions+%283x%2B1%29%2F%28%28x-1%29%5E3%28x%2B1%29%29
how to make the work less tedious: use linear lagebra
linear algebra lol
:P
if you can use Cramer's rule for large systems that is one way, but I don't suppose you've studied that yet
in cases like this it is annoying because you can't just put certain values of x to find the coefficients

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