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Thread: Partial fractions in chemical kinetics

  1. #1
    Kew
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    Question Partial fractions in chemical kinetics

    Hello,
    I ' m studying chemical kinetics and found one mathematical problem.
    Please, can you help me ?
    I found in book, that the expression 1/(a-x)2(b-x) is decomposed into partial fractions like:
    1/(a-x)2(b-x) = (R1x+R2)/(a-x)2 + R3/(b-x)
    Why is wrong next expression? :
    1/(a-x)2(b-x) = R1/(a-x) + R2/(a-x)2 + R3/(b-x)

    a,b
    are
    initial concentrations (>0)

    For sure, I've attached the handwritten text.

    Thank you very much for help


    Kevin




    Partial fractions in chemical kinetics-19179655_1632105840133571_939057859_o.jpg
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  2. #2
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    Re: Partial fractions in chemical kinetics

    the two are equivalent since

    \frac{R_1x+R_2}{(x-a)^2}=\frac{R_1}{x-a}+\frac{a R_1+R_2}{(x-a)^2}
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