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Math Help - Partial fractions

  1. #1
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    Question Partial fractions

    Hi i got the following:

    5x^2 + 5x + 5 = (Ax+B)(x+2) + C(x^2 + 1)

    Now i got C = 3
    But confused how to get A and B
    I know you have to equate both sides for x^2
    so:

    5=[confused]
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by taurus View Post
    Hi i got the following:

    5x^2 + 5x + 5 = (Ax+B)(x+2) + C(x^2 + 1)

    Now i got C = 3
    But confused how to get A and B
    I know you have to equate both sides for x^2
    so:

    5=[confused]
    You expand the left hand side and collect terms of like order in x, then
    you equate coefficients of like powers of x on each side of the equation
    to give a set of three simultaneous equations in A, B and C.

    Doing this we have:

    5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

    so we have:

    ..A +. B ..... = 5
    2A + .B ..... = 5
    ...... 2B + C = 5

    Which you now solve.

    RonL
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  3. #3
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    5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

    still confused how you got that?
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  4. #4
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    Look at the numerical coefficients of both sides.

    Coefficient of x^2 on the LHS is 5, so belongs it to a+b; coefficient of x on the LHS is 5, so belongs it to 2a+b; coefficient 5 on the LHS is 5, so belongs it to 2b+c.

    After that, you'll get CaptainBlack's system, which is easy to solve.
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  5. #5
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    but how did you get these:

    (A+B)x^2 + (2A+B)x + (2B+C)
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  6. #6
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    Question

    ok i get it, but now how do i solve for A and B?
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