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Math Help - fraction decomposition

  1. #1
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    fraction decomposition

    (3x^2+7) / ( (x-1)(x^2+2x+5) )
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  2. #2
    Jen
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    Quote Originally Posted by cityismine View Post
    (3x^2+7) / ( (x-1)(x^2+2x+5) )
    Your set up will look like this,

    \frac{3x^2+7}{(x-1)(x^2+2x+7}=\frac{A}{(x-1)}+\frac{Bx+C}{(x^2+2x+5)}

    Clearing the denominators gives us,

    3x^2+7=A(x^2+2x+5)+(Bx+c)(x-1)

    Test a couple of values of x like x=1 to solve for A , B and C

    Your solution should come out as,

    A=\frac{5}{4} \\\ B= \frac{7}{4} \\\ and \\\ C=-\frac{3}{4}

    Which would give you,

    \frac{5}{4(x-1)}+\frac{7x+3}{4(x^2+2x+5)}

    Hope that helps!!
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  3. #3
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    I figured it out, my answer matches yours, so it's right. thx,
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