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Math Help - comparing coefficients

  1. #1
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    comparing coefficients

    Ok just quickly what happens in this case


    A + B = 3
    -2A - 2B = -2

    Both terms disapear when I add them together.. what do i need to do to get the values of A and B??

    2A +2B = 6
    -2A -2B = -2

    0 = 4
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  2. #2
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    What was the original question?

    Divide the second equation by -2 and we have: \begin{aligned} A + B & = 3 \\ A + B & = 1 \end{aligned}

    Now think about this logically. How can two numbers add up to 3 and 1 at the same time?
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  3. #3
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    I see...

    I was doing partial fractions,

    int (3-2x) / (x^2-4x+4)

    int (3-2x) / (x-2)(x-2)

    A(x-2)+B(x-2)

    Numerator: (A+B)x + (-2A-2B)

    I'm guessing I've done something wrong here..
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  4. #4
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    You have to combine the linear factors in the denominator into a single power: \int \frac{3-2x}{x^2 - 4x + 4} \ dx  = \int \frac{3-2x}{(x-2)^2} \ dx

    Then apply partial fraction decomposition: \frac{3 - 2x}{(x-2)^2} = \frac{A}{x-2} + \frac{B}{(x-2)^2}

    Try it now.
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  5. #5
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    Ah right I get it, thanks alot!!
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