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Math Help - Partial fraction

  1. #1
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    Partial fraction

    find the values of A,B and C such that



    i see that it is repeated linear, but the x^2+4 is confusing me.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Partial fraction

    Write

    \frac{2x-3}{(x+1)(x^2+4)}=\frac{A(x^2+4)+(Bx+C)(x+1)}{(x+1)  (x^2+4)}

    and identify numerators.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: Partial fraction

    "repeated linear" -?? I've never heard of that. Multiply by the LCD to get
     2x - 3 = A(x^2 + 4) + (Bx + C)(x + 1)

     2x - 3 = Ax^2 + 4A + Bx^2 + (B + C)x + C

     2x - 3 = (A + B)x^2 + (B + C)x + (4A + C)

    Now equate coefficients.
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  4. #4
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    Re: Partial fraction

    Quote Originally Posted by TheChaz View Post
    "repeated linear" -?? I've never heard of that. Multiply by the LCD to get
     2x - 3 = A(x^2 + 4) + (Bx + C)(x + 1)
    ...
    Equate the numerators in FernandoRevilla's equation, and the result is exactly what you have in the above quote from your post.
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  5. #5
    Super Member TheChaz's Avatar
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    Re: Partial fraction

    True, though I'm not sure I get your point.

    Expressing the terms with a common denominator and determining what's left after multiplying by the LCD are procedurally almost identical...
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  6. #6
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    Re: Partial fraction

    Quote Originally Posted by TheChaz View Post
    True, though I'm not sure I get your point.

    Expressing the terms with a common denominator and determining what's left after multiplying by the LCD are procedurally almost identical...
    Sorry about that Chaz. I didn't look at OP closely enough & thought that somehow you were referring to FernandoRevilla's Post.
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