For the following rational functions, find the partial fraction decomposition
3x
x^3 - 2x^2 - x + 2
x^2 - x +1
x^3 - x^2 + x -1
Any assistance would be greatly appreciated!
Both denominators can be factored here is the first one
$\displaystyle x^3-2x^2-x+2=x^2(x-2)-1(x-2)=(x-2)(x^2-1)=(x-2)(x-1)(x+1)$
This has three linear factors with no repeates
$\displaystyle \frac{A}{x-2}+\frac{B}{x-1}+\frac{C}{x+1}=\frac{3x}{(x-2)(x-1)(x+1)}$
Show us what you can do from here