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Core 4 - Improper Fractions as Partial Fractions - Help! Watch

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    Hello,

    I'm having some trouble with representing improper partial fractions where the power on the top is either greater than or equal to the power on the bottom as a partial fraction. I am not using the division method and am instead using the method found on example two below:

    http://kineticmaths.com/index.php?ti...oper_Fractions

    The questions:
    Express the following as a partial fraction:

    Number One

    Number Two

    Write the following algebraic fractions as partial fractions:






    Here's my working for number two:

    The power on the top is (2) and the power on the bottom is (2) and so the fraction is improper.

    Factorise x^2 + 2x-3 to get (x-1)(x+3) and then rewrite:

    (2) - (2) = (0) so we are expecting a constant term A.

    Then we do B divided by the first bracket (X-1) and C divided by the second (X+3) to get

    2x^2+2x-8 = A + B / (X-1) + C / (X+3)

    Then simplify..

    2x^2+2x-8 = A(X-1)(X+3)+B(X+3)+C(X-1)


    I then subbed in X = 1 & X = -3 to get:

    B = -1 / C = -1 and subbed in B & C to find A which was 2 to finish with this answer which is wrong.




    Can anyone help out / give me some explanation to your methods?

    Thanks.
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    (Original post by luciferhf)
    Hello,

    I'm having some trouble with representing improper partial fractions where the power on the top is either greater than or equal to the power on the bottom as a partial fraction. I am not using the division method and am instead using the method found on example two below:

    http://kineticmaths.com/index.php?ti...oper_Fractions

    The questions:
    Express the following as a partial fraction:


    Number One

    Number Two

    Write the following algebraic fractions as partial fractions:






    Here's my working for number two:

    The power on the top is (2) and the power on the bottom is (2) and so the fraction is improper.

    Factorise x^2 + 2x-3 to get (x-1)(x+3) and then rewrite:

    (2) - (2) = (0) so we are expecting a constant term A.

    Then we do B divided by the first bracket (X-1) and C divided by the second (X+3) to get

    2x^2+2x-8 = A + B / (X-1) + C / (X+3)

    Then simplify..

    2x^2+2x-8 = A(X-1)(X+3)+B(X+3)+C(X-1)


    I then subbed in X = 1 & X = -3 to get:

    B = -1 / C = -1 and subbed in B & C to find A which was 2 to finish with this answer which is wrong.




    Can anyone help out / give me some explanation to your methods?

    Thanks.
    You've subtracted your last term so you've said C=+1 to the computer
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    (Original post by h3rmit)
    You've subtracted your last term so you've said C=+1 to the computer

    o.O well in that case looks like I may have been correct. Can somebody still go through the first question with the same method?
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    (Original post by luciferhf)
    o.O well in that case looks like I may have been correct. Can somebody still go through the first question with the same method?
    I got the right answer with the same method according to
    http://www.quickmath.com/#c=simplify...2F(2(x-2))%2B1
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    (Original post by h3rmit)
    I got the right answer with the same method according to
    http://www.quickmath.com/#c=simplify...2F(2(x-2))%2B1
    Thanks! Do you mind telling me what were your values that went under A, B & C?

    The first line of working.
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    (Original post by luciferhf)
    Thanks! Do you mind telling me what were your values that went under A, B & C?

    The first line of working.
    x, (x-2), 1 if you mean x's
 
 
 
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