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Math Help - [SOLVED] partial fraction decomposition

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    [SOLVED] partial fraction decomposition

    i have to write the partial fraction decomposition of this and i really don't know how to begin.

    x^2 - x / x^2 + x +1
    Last edited by mr fantastic; January 5th 2009 at 06:28 PM. Reason: Restored question after deletion by the OP
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    Quote Originally Posted by jbeybey View Post
    i have to write the partial fraction decomposition of this and i really don't know how to begin.

    x^2 - x / x^2 + x +1
    Start by noting that:

    1. \frac{x^2 - x}{x^2 + x + 1} = 1 - \frac{2x + 1}{x^2 + x + 1}.

    2. x^2 + x + 1 is an irreducible quadratic (what do you class notes or textbook say that you do in this case.....?)
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    Quote Originally Posted by jbeybey View Post
    i have to write the partial fraction decomposition of this and i really don't know how to begin.

    x^2 - x / x^2 + x +1
    Since the numerator has the same degree as the denominator, the first thing will want to do is divide it out.
    \frac{x^2- x}{x^2+ x+ 1}= 1- \frac{2x+1}{x^2+ x+1}

    Since the denominator cannot be factored (by the quadratic formula it has no real roots), that is the "partial fraction decomposition".
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