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Thread: Decompose

  1. #1
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    1 math question

    Identify the form of the partial fraction decomposition. Do not solve for the constants. 8x2+7x
    (x+5)3

    A: A + Bx + Cx2
    X+5 (x+5)2 (x+5)3

    B: A + B + C
    X+5 (x+5)2 (x+5)3

    C: Ax2 + Bx + C
    (x+5)3

    D: A + Bx+C
    X+5 (x+5)2


    Identify the conic section with the given equation.
    5x2-6y2-9x+2y+3=0


    p.s. all the two and threes after the par. and x's are supposed to be raised to that power!
    Last edited by Lane; Jul 6th 2006 at 08:33 PM.
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  2. #2
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    Hello, Lane!


    Identify the form of the partial fraction decomposition for: .$\displaystyle \frac{8x^2+7x}{(x+5)^3}$

    $\displaystyle A\!:\;\frac{A}{x+5} + \frac{Bx}{(x+5)^2} + \frac{Cx^2}{(x+5)^3}
    $ . . . $\displaystyle B\!:\;\;\frac{A}{x+5} + \frac{B}{(x+5)^2} + \frac{C}{(x+5)^3}$

    . . . $\displaystyle C\!:\;\;\frac{Ax^2 + Bx + C}{(x+5)^2}$. . . . . $\displaystyle D\!:\;\;\frac{A}{x+5} + \frac{Bx+C}{(x+5)^2}$

    With repeated linear factors,
    . . we need a linear fraction for "each power".

    Since $\displaystyle x+5$ is cubed, the denominators must be: .$\displaystyle x+5,\;(x+5)^2,\;(x+5)^3$

    The answer is choice $\displaystyle B.$


    Last edited by Soroban; Jul 7th 2006 at 06:53 AM.
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  3. #3
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    Hello, Lane!


    We can "eyeball" the second one . . .


    Identify the conic section: .$\displaystyle 5x^2-6y^2-9x+2y+3\:=\:0$

    Since the $\displaystyle x^2$-term and the $\displaystyle y^2$-term have opposite signs,

    . . the conic is a $\displaystyle \text{hyperbola.}$

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