# Reducing final answer of laplace transform

## 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...

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## 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...

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 $(s+4)^4(s-4)^4=[(s+4)(s-4)]^4=(s^2-16)^4$

Yeh thats what i meant.

Awsome, cheers for the help!

thought it was something like that