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Math Help - Partial fractions

  1. #1
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    Partial fractions

    1. a) Express (x+3)/x(x-1) in terms of partial fractions

    b) Find ∫(x+3)/x(x-1)dx

    Not sure if i need to expand the denominator in a?

    really have no idea how to do b!
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  2. #2
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    Quote Originally Posted by djmccabie View Post
    1. a) Express (x+3)/x(x-1) in terms of partial fractions

    b) Find ∫(x+3)/x(x-1)dx

    Not sure if i need to expand the denominator in a?

    really have no idea how to do b!
    \frac{x+3}{x^2(x-1)}

    = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}
    Last edited by mathaddict; March 2nd 2009 at 08:28 AM. Reason: mistake .
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  3. #3
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    Quote Originally Posted by djmccabie View Post
    1. a) Express (x+3)/x(x-1) in terms of partial fractions

    b) Find ∫(x+3)/x(x-1)dx

    Not sure if i need to expand the denominator in a?

    really have no idea how to do b! that's why you do (a) first
     <br />
\frac{x+3}{x^2(x-1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}<br />

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

    let x = 1 ... C = 4

    let x = 0 ... B = -3

    let x = 2 ... A = -4


    \int \frac{x+3}{x^2(x-1)} \, dx = \int -\frac{4}{x} - \frac{3}{x^2} + \frac{4}{x-1} \, dx<br />
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  4. #4
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    hi just a question. When you let x=2, what happens to B and C ?
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  5. #5
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    Replace them with the values you already had: B= -3, C= 4.
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