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Math Help - Need help with partial fraction

  1. #1
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    Question Need help with partial fraction

    Need help with partial fraction-9fobb7.png

    I get stuck at the ((Ax+B)/(x^2+1)) + ((Cx+D)/(x^2+2)) part.

    How exactly do we solve for these variables A, B, C, and D? If I plug in zero the equation would become:

    3x^3 - x^2 + 6x - 4 = (Ax+B)(x^2+2) + (Cx+D)(x^2+1)

    3(0)^3 - (0)^2 + 6(0) - 4 = (A(0)+B)((0)^2+2) + (C(0)+D)((0)^2+1)

    That would leave me with: -4 = 2B + D.

    I have tried multiplying it out and setting it equal to the coefficient such as this:

    A + C = 3
    B + D = -1
    2A + C = 6
    2B + D = -4

    But to no avail. Please help me figure out how to solve for these variables. Thanks in advance.
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  2. #2
    MHF Contributor harish21's Avatar
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    You should remember simultaneous equations from your algebra classs

    So you have


    2A+C=6....(I)

    A+C=3......(II)

    Subtract Equation(II) from Equation (I), and you'll have:

    2A-A+C-C = 6-3 \implies A=3,

    And with A =3, you can find the value of C, which is .....

    Then Use the same approach in the equations involving B and D.

    B + D = -1

     2B + D = -4
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