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Math Help - Partial Fractions

  1. #1
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    Partial Fractions

    ∫(4x-11x+4)/(x-3x+2x) dx

    i know the bottom part breaks up into
    x(x-3x+2) = x(x-2)(x-1)

    where do i go form there?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by hlpplz View Post
    ∫(4x-11x+4)/(x-3x+2x) dx

    i know the bottom part breaks up into
    x(x-3x+2) = x(x-2)(x-1)

    where do i go form there?
    \frac {4x^2 - 11x + 4}{x^3 - 3x^2 + 2x} = \frac {4x^2 - 11x + 4}{x(x - 2)(x - 1)} = \frac Ax + \frac B{x - 2} + \frac C{x - 1}

    multiplying both sides of the equation by the LCD, we have:

    4x^2 - 11x + 4 = A(x - 2)(x - 1) + Bx(x - 1) + Cx(x - 2)

    now can you finish?
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by hlpplz View Post
    ∫(4x-11x+4)/(x-3x+2x) dx

    i know the bottom part breaks up into
    x(x-3x+2) = x(x-2)(x-1)

    where do i go form there?
    ∫(4x-11x+4)/(x-3x+2x)

    = \int{\frac{A}{x} +\frac{B}{x-2} +\frac{C}{x-1}}

    Find A B & C And then integrate

    its too late
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  4. #4
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    ok so i multiplied by the LCD and got

    4x-11x+4 = A(x-2)(x-1) + B(x)(x-1) + C(x)(x-2)
    4x-11x+4 = A(x-3x+2) + B(x-x) + C(x-2x)

    isolating x = A + B + C = 4
    isolating x = -3A - B - 2C = -11
    isolating # = 2A = 4

    solving for A,B,C i got

    A= 2, B=-7, C=9

    ∫ A/x + B/(x-2) + C/(x-1) dx

    ∫ 2/x - 7/(x-2) + 9/(x-1) dx

    2∫ 1/x - 7∫ 1/(x-2) + 9∫ 1/(x-1) dx

    2ln⎮x⎮ - 7ln⎮x-2⎮ + 9ln⎮x-1⎮

    Good?
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by hlpplz View Post
    ok so i multiplied by the LCD and got

    4x-11x+4 = A(x-2)(x-1) + B(x)(x-1) + C(x)(x-2)
    4x-11x+4 = A(x-3x+2) + B(x-x) + C(x-2x)

    isolating x = A + B + C = 4
    isolating x = -3A - B - 2C = -11
    isolating # = 2A = 4

    solving for A,B,C i got

    A= 2, B=-7, C=9

    ∫ A/x + B/(x-2) + C/(x-1) dx

    ∫ 2/x - 7/(x-2) + 9/(x-1) dx

    2∫ 1/x - 7∫ 1/(x-2) + 9∫ 1/(x-1) dx

    2ln⎮x⎮ - 7ln⎮x-2⎮ + 9ln⎮x-1⎮ +c

    Good?
    Yes
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  6. #6
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    Thank you very much
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