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Math Help - Help Partial Fractions

  1. #1
    Junior Member Cthul's Avatar
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    Help Partial Fractions

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

    When I expand this, I can't eliminate to get one variable to get the variable.
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  2. #2
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    Quote Originally Posted by Cthul View Post
    \frac{1+x}{x(1+x^{2})}

    When I expand this, I can't eliminate to get one variable to get the variable.
    Write it as

    \frac{A}{x} + \frac{Bx + C}{1 + x^2} = \frac{1 + x}{x(1 + x^2)}

    \frac{A(1 + x^2) + (Bx + C)x}{x(1 + x^2)} = \frac{1 + x}{x(1 + x^2)}

    A(1 + x^2) + (Bx + C)x = 1 + x

    A + Ax^2 + Bx^2 + Cx = 1 + x

    (A + B)x^2 + Cx + A = 0x^2 + x + 1.


    Equating coefficients of like powers of x gives

    A + B = 0, C = 1, A = 1.

    So B = -1.


    Therefore:

    \frac{1}{x} + \frac{1 - x}{1 + x^2} = \frac{1 + x}{x(1 + x^2)}.
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  3. #3
    Junior Member Cthul's Avatar
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    Thank you, problem solved. I understand how now.
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