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Math Help - need help for partial fraction

  1. #1
    Member moonnightingale's Avatar
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    need help for partial fraction

    how can i do partial fraction for this equation

    2/(x^2 +.786x + .212)

    plz help

    what will happend if there is another term like this in denominator

    2/((x^2 +.786x + .212)(x^2+.23x+.9))

    thanks
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by moonnightingale View Post
    how can i do partial fraction for this equation

    2/(x^2 +.786x + .212)

    plz help

    what will happend if there is another term like this in denominator

    2/((x^2 +.786x + .212)(x^2+.23x+.9))

    thanks
    For the first one since the discriminant is negative

    b^2-4ac=(.786)-4(1)(.212) < 0 the quadratic is irreducible.

    So over the real numbers there is not a partial fraction decomposition.

    Again fro the 2nd one both quadratic factors are irreducible we get that

    \dipslaystyle \frac{Ax+B}{x^2 +.786x + .212}+\frac{Cx+D}{x^2+.23x+.9}=\frac{2}{(x^2 +.786x + .212)(x^2+.23x+.9)}
    Now multiply the LCD to get

    \displaystyle (Ax+B)(x^2+.23x+.9)+(Cx+D)(x^2 +.786x + .212)=2

    Now expand everything out and collect all of the x's to get

    (A+C)x^3+(.23A+B+.786C+D)x^2+(.9A+.23B+.212C+.786D  )x+(.9B+.212D)=2=0x^3+0x^2+0x+2

    Now equate the coefficients to get a system of 4 equations in 4 unknowns.
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