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Math Help - Partial Fractions

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    Partial Fractions

    s = \frac{s^2+8}{(s^2+4)(s^2+9)}

    A(s^2+9) + B(s^2+4) = s^2+8

    Uncertain of what number to substitute to solve ?
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  2. #2
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    Quote Originally Posted by louboutinlover View Post
    s = \frac{s^2+8}{(s^2+4)(s^2+9)}

    A(s^2+9) + B(s^2+4) = s^2+8

    Uncertain of what number to substitute to solve ?
    You can make some equations by comparing coefficients
    Last edited by e^(i*pi); April 30th 2009 at 02:04 PM. Reason: changing x for s
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    how do you compare coefficients ?
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    Quote Originally Posted by louboutinlover View Post
    s = \frac{s^2+8}{(s^2+4)(s^2+9)}

    A(s^2+9) + B(s^2+4) = s^2+8

    Uncertain of what number to substitute to solve ?
    ANY numbers will do! Putting any 2 numbers in for s will give two equations for A and B. For example, if s= 0, A(0+ 9)+ B(0+ 4)= 0+ 8 or 9A+ B= 8. If s= 1, A(1+ 9)+ B(1+ 4)= 1+ 8 or 10A+ 5B= 9.
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    Quote Originally Posted by louboutinlover View Post
    how do you compare coefficients ?
    You had A(s^2+9) + B(s^2+4) = s^2+8. Multiply it out: As^2+ 9A+ Bs^2+ 4B= s^2+ 8
    (A+ B)s^2+ (9A+ 4B)= s^2+ 8
    The coefficient of s^2 is A+ B on one side, 1 on the other: you must have A+ B= 1. The coefficient of s is 0 on both sides (whew!). The constant term is 9A+ 4B on one side and 8 on the other. You must have 9A+ 4B= 8.
    Last edited by HallsofIvy; May 1st 2009 at 04:22 AM.
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