Simplifying Inverse Laplace Function

[polarmystery]

Homework Statement

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.

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

Homework Equations

none

The Attempt at a Solution

I couldn't arrive at anything past this

 

[HallsofIvy]

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.

 

[polarmystery]

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