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Reducing final answer of laplace transform

  1. May 19, 2009 #1
    1. The problem statement, all variables and given/known data
    The problem is not getting the answer to the laplace transform but instead reducing my answer so i dnt lose marks.

    If i work out the laplace transform of:
    L(t^3 * sinh(4t)) to be
    3!/(2(s- 4)^4)- 3!/(s(s+ 4)^4) then how do i add these to get a single fraction? Its doing my head in

    3. The attempt at a solution
    I know something has to be multiplied but i have no idea what it is...

    Thanks in advance!
  2. jcsd
  3. May 19, 2009 #2


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    Gold Member

    Did you mean [itex]\mathcal{L}[t^3 \sinh(4t)]=\frac{3!}{2(s- 4)^4}- \frac{3!}{2(s+ 4)^4}[/itex]?

    If so, the first thing to do would be get rid of the factorials; [itex]3!=3*2[/itex] and then cancel the 2 in the denominators.

    Next, multiply the first fraction (numerator and denominator) by [itex](s+4)^4[/itex] and the second fraction (numerator and denominator) by [itex](s-4)^4[/itex]

    Then expand out the numerator and simplify.

    You can also simplify the common denominator by noting that [itex](s+4)^4(s-4)^4=[(s+4)(s-4)]^4=(s^2-16)^4[/itex]
  4. May 19, 2009 #3
    Yeh thats what i meant.

    Awsome, cheers for the help!

    thought it was something like that
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