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Math Help - Partial Fractions with e^x on Top

  1. #1
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    Partial Fractions with e^x on Top

    To put it bluntly, how do I go about solving:

    \frac{e^{-10s}}{(s + 3)(s+2)}

    I'm doing a Laplace Transform of the below, and can't work out how to solve the partial fraction I get (i.e. the above partial fraction). I know how to solve partial fractions normally, it's just the e^{-10s} that's giving me trouble.

    x'' + 5x' + 6x(t) = \delta(t-10)
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  2. #2
    Moo
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    Hello,

    \frac{e^{10s}}{(s+3)(s+2)}=e^{10s} \cdot \left(\frac{1}{(s+3)(s+2)}\right)

    Now you can do the partial fractions decomposition ^^
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  3. #3
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    Interesting. Probably the stupidest I've felt for months now :P

    Wait, in which case, I can't factor out e^{s} here:

    \frac{e^{-s} + 2s + 7} {(s+1)^2}

    Is there a general method when you have a non-polynomial function on top?
    Last edited by bumcheekcity; December 9th 2008 at 11:57 AM.
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  4. #4
    Moo
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    Quote Originally Posted by bumcheekcity View Post
    Interesting. Probably the stupidest I've felt for months now :P
    haha ! it happens to everybody to forget easy stuff !
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