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Math Help - Getting stuck with partial fractions

  1. #1
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    Getting stuck with partial fractions

    Ok this is driving me nuts so I hope someone can help!

    8s^2-4s+12/s(s^2+4)

    I am using partial fraction decomposition of this to find the A, B and C. So 8s^2-4s+12=A/s +[B/(s-0)^2+4] +[C/(s-0)^2+4] and thus 8s^2-4s+12=A[(s-0)^2+4]+Bs+Cs

    When I use the sub values in for S method, I am subbing in a 0 for the S, and this gets me 12=4A so A=3. BUT when you do it with the expand and compare method, I get A=8.

    Where am I going wrong here??
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  2. #2
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    {12\over s(s^2+4)} = {3\over s} - {3s \over s^2 + 4}. Or maybe you want {8s^2-4s +12\over s(s^2+4)} = {3\over s} + {5s-4\over s^2 + 4}, I can't really tell, sorry.
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  3. #3
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    <br />
\frac{8s^2-4s+12}{s(s^2+4)}=\frac{A}{s}+\frac{Bs+C}{s^2+4}=\f  rac{3}{s}+\frac{5s-4}{s^2+4}<br />
.
    There is no solution for
    <br />
\frac{8s^2-4s+12}{s(s^2+4)}\ne\frac{A}{s}+\frac{B}{s^2+4}=\fr  ac{A(s^2+4)+Bs}{s(s^2+4)}=\frac{As^2+Bs+4A}{s(s^2+  4)}<br />
    A=8
    B=-4
    4A=12 \Rightarrow A=3
    because the same time must be A=8 and A=3 what is impossible.
    Last edited by zzzoak; April 10th 2010 at 03:58 PM.
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