# Inverse Laplace?

1. Oct 6, 2011

### polarmystery

1. The problem statement, all variables and given/known data

Any way to reduce this function for simplification? (Trying to find the reverse Laplace function) I found this function after doing a circuit analysis on a transmission line.

$$\frac{s^2RC+sL}{s^2RC+sL+R}$$

2. Relevant equations

none

3. The attempt at a solution

I couldn't arrive at anything past this

2. Oct 6, 2011

### HallsofIvy

Staff Emeritus
Well, seeing "$s^2RC+ sL$" in both numerator and denominator, the first thing I would do is divide $s^2RC+ sL+ R$ into $s^2RC+ sL$. Obviously, it will go into it once with remainder $(s^2RC+ sL)- (s^2RC+ sL+ R)= -R$.

That is
$$\frac{s^2RC+ sL}{s^2RC+ sL+ R}= 1-\frac{R}{s^2RC+ sL+ R}$$

Now, if s is the variable, complete the square in the denominator.

3. Oct 6, 2011

### polarmystery

holy cow that was quick. Many thanks. I think that works out.