Partial Fraction Decomposition

**speckmagoo** · April 26th 2009, 07:49 AM

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!

**TheEmptySet** · April 26th 2009, 07:53 AM

Originally Posted by speckmagoo

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

$x^3-2x^2-x+2=x^2(x-2)-1(x-2)=(x-2)(x^2-1)=(x-2)(x-1)(x+1)$

This has three linear factors with no repeates

$\frac{A}{x-2}+\frac{B}{x-1}+\frac{C}{x+1}=\frac{3x}{(x-2)(x-1)(x+1)}$

Show us what you can do from here

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