Reducing final answer of laplace transform

[xtipd]

Homework Statement

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

The Attempt at a Solution

I know something has to be multiplied but i have no idea what it is...

Thanks in advance!

 

[gabbagabbahey]

Homework Statement

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

The Attempt at a Solution

I know something has to be multiplied but i have no idea what it is...

Thanks in advance!

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

If so, the first thing to do would be get rid of the factorials; 3!=3*2 and then cancel the 2 in the denominators.Next, multiply the first fraction (numerator and denominator) by (s+4)^4 and the second fraction (numerator and denominator) by (s-4)^4

Then expand out the numerator and simplify.

You can also simplify the common denominator by noting that (s+4)^4(s-4)^4=[(s+4)(s-4)]^4=(s^2-16)^4

 

[xtipd]

Yeh that's what i meant.

Awsome, cheers for the help!

thought it was something like that