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Math Help - Partial Fractions

  1. #1
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    Partial Fractions

    I understand the main idea about partial fractions. We were given this 'challenge problem', and this definitely doesn't look
    what are the coefficients A B C D E for

    (5x^4 - 10x^3 + x^2 - 24x + 18) /
    ((x-4) ((x^2 +1)^2))

    using: A/x-4 + Bx+C/x^2+1 + Dx+E/ ((x^2+1)^2)
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  2. #2
    MHF Contributor
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    Quote Originally Posted by C.C. View Post
    I understand the main idea about partial fractions. We were given this 'challenge problem', and this definitely doesn't look
    what are the coefficients A B C D E for

    (5x^4 - 10x^3 + x^2 - 24x + 18) /
    ((x-4) ((x^2 +1)^2))

    using: A/x-4 + Bx+C/x^2+1 + Dx+E/ ((x^2+1)^2)
    HI

    \frac{5x^4-10x^3+x^2-24x+18}{(x-4)(x^2+1)^2}=\frac{A}{x-4}+\frac{Bx+C}{x^2+1}+\frac{Dx+E}{(x^2+1)^2}

    Multiply the whole thing by (x-4)

    \frac{5x^4-10x^3+x^2-24x+18}{(x^2+1)^2}=A+\left(\frac{Bx+C}{x^2+1}+\fra  c{Dx+E}{(x^2+1)^2}\right)(x-4)

    Substitute x=4 ,you can get A . THen substitute other values : 0 , 1 , -1 etc , values which make your calculation convenient . You will need to solve these simultaneous equations to get the rest . I haven tried yet , you give it a try and see whether it works or not . GOod luck .
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