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Math Help - Calculus II- Partial Fractions

  1. #1
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    Question Calculus II- Partial Fractions

    I'm struggling figuring out how to break apart the fraction and what to use in the numerator (Ax+B, A+B+C?)
    help!

    INTEGRAL 4x^2 +36 / x(x^2 -9)


    thanks
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  2. #2
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    Quote Originally Posted by imarockstar858 View Post
    I'm struggling figuring out how to break apart the fraction and what to use in the numerator (Ax+B, A+B+C?)
    help!

    INTEGRAL 4x^2 +36 / x(x^2 -9)
    \frac{4x^2+36}{x(x+3)(x-3)} = \frac{A}{x} + \frac{B}{x+3} + \frac{C}{x-3}<br />

    4x^2 + 36 = A(x+3)(x-3) + Bx(x-3) + Cx(x+3)<br />

    let x = 0 ...

    36 = -9A ... A = -4

    let x = -3 ...

    72 = 18B ... B = 4

    let x = 3 ...

    72 = 18C ... C = 4


    4 \int -\frac{1}{x} + \frac{1}{x+3} + \frac{1}{x-3} \, dx
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  3. #3
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    Thank you so much! I didn't know what "alphabet" letters to put. Thanks so much!
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  4. #4
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    Talking

    Quote Originally Posted by imarockstar858 View Post
    I didn't know what "alphabet" letters to put.
    The particular letters you use are up to you!

    This is really a topic from algebra, but it's usually only touched on in calculus, with the assumption (usually wrong, in my experience) that the student is already familiar with the technique, which can be frustrating!

    For a review with worked examples, look through a few online lessons.
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