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Math Help - partial fraction

  1. #1
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    partial fraction

    Express each of the following in partial fraction .

    (a) \frac{x^2-1}{x^2(2x+1)}

    Is x^2 (denominator) , considered as a repeated linear factor ?

    (b) \frac{x^3+3}{(x+1)(x-1)}

    i have tried long division for this question but it doesn't work .
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    Express each of the following in partial fraction .

    (a) \frac{x^2-1}{x^2(2x+1)}

    Is x^2 (denominator) , considered as a repeated linear factor ?
    Yes.

    So \frac{x^2-1}{x^2(2x+1)} = \frac{Ax+B}{x^2} + \frac{C}{2x+1}

    Get A,B and C by cross multiplying and comparing coefficients.

    Quote Originally Posted by mathaddict View Post
    (b) \frac{x^3+3}{(x+1)(x-1)}

    i have tried long division for this question but it doesn't work .
    It should. Divide x^3 + 3 by x^2 - 1. You will see that:
    \frac{x^3+3}{x^2 - 1} = x + \frac{ x+3 }{x^2 - 1}

    Now do a partial fraction decomposition for \frac{x+3}{x^2 - 1}
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    Yes.

    So \frac{x^2-1}{x^2(2x+1)} = \frac{Ax+B}{x^2} + \frac{C}{2x+1}

    Get A,B and C by cross multiplying and comparing coefficients.
    Can i do it this way ..
    \frac{x^2-1}{x^2(2x+1)}
    = \frac{A}{x}+\frac{B}{x^2}+\frac{C}{2x+1}
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  4. #4
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    Quote Originally Posted by mathaddict View Post
    Can i do it this way ..
    \frac{x^2-1}{x^2(2x+1)}
    = \frac{A}{x}+\frac{B}{x^2}+\frac{C}{2x+1}
    Yes.
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