# Reducing final answer of laplace transform

• xtipd
In summary, the person is struggling with reducing their answer for a Laplace transform to a single fraction. They mention trying to multiply by a certain factor but are unsure of what it should be. Another person offers a solution involving simplifying factorials and expanding out the numerator. The person is grateful for the help and confirms that their initial idea was correct.

## 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...

xtipd said:

## 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 that's what i meant.

Awsome, cheers for the help!

thought it was something like that

## What is the Laplace transform and when is it used?

The Laplace transform is a mathematical technique used to convert a function of time into a function of complex frequency. It is often used in engineering and physics to solve differential equations and analyze systems in the frequency domain.

## Why is the final answer of Laplace transform reduced?

The final answer of Laplace transform is reduced in order to simplify and solve complex equations. By reducing the final answer, we can easily identify the behavior and characteristics of a system in the frequency domain.

## What is the process of reducing the final answer of Laplace transform?

The process of reducing the final answer of Laplace transform involves applying various mathematical techniques such as partial fraction decomposition, inverse Laplace transform, and residue theorem. These techniques help to simplify the expression and solve for the final answer.

## What are the benefits of reducing the final answer of Laplace transform?

Reducing the final answer of Laplace transform allows us to analyze and understand the behavior of a system in the frequency domain. It also helps us to solve complex equations and make predictions about the system's response to different inputs.

## Are there any limitations to reducing the final answer of Laplace transform?

While reducing the final answer of Laplace transform can help us understand and analyze a system, it may not always provide an accurate representation of the system's behavior. Additionally, the process of reducing can be time-consuming and may not always be feasible for complex systems.