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Math Help - partial fractions #2

  1. #1
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    partial fractions #2

    Similarly, to my previous problem. I solved the problem and got an answer, but it says it's the incorrect answer.

    The problem is:



    I set the equation to be:

    x^3 + 17 = A(x+1) + B(x+3)

    I solved for A first and got 5.

    I then went back and solved for B and got 8.

    This would result in the partial fraction of:



    I then integrated and got:

    5 ln |x+1| + 8 ln |x+3|

    Can anyone show me how it is correctly done?

    Thank you.
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  2. #2
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    Quote Originally Posted by abilitiesz View Post
    Similarly, to my previous problem. I solved the problem and got an answer, but it says it's the incorrect answer.

    The problem is:



    I set the equation to be:

    x^3 + 17 = A(x+1) + B(x+3)

    I solved for A first and got 5.

    I then went back and solved for B and got 8.

    This would result in the partial fraction of:



    I then integrated and got:

    5 ln |x+1| + 8 ln |x+3|

    Can anyone show me how it is correctly done?

    Thank you.
    note that if you add those two fractions, you will not get an x^3 term in the numerator.


    start by doing long division ...

    \frac{x^3+17}{x^2+4x+3} = x - 4 + \frac{13x+29}{x^2+4x+3}<br />

    now do partial fractions with the last term.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    note that if you add those two fractions, you will not get an x^3 term in the numerator.


    start by doing long division ...

    \frac{x^3+17}{x^2+4x+3} = x - 4 + \frac{13x+29}{x^2+4x+3}<br />
    Ah, thank you. I figured it out with your advice.
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