Getting stuck on a simple inverse Laplace transform. How do I massage this fraction?

I'm having some difficulty with what should be a simple (one sided) inverse Laplace transform:

Now, I know the answer is

I'm just not sure how to get there. I'm not looking to apply the definition - I'm looking to massage the fraction into standard transform pairs or use standard properties of the transform.

It seems to me that I need to accomplish this:

I'll probably kick myself for this, but what am I missing?

Re: Getting stuck on a simple inverse Laplace transform. How do I massage this fract

you can get it like this easily,

then remember that

and and where

Re: Getting stuck on a simple inverse Laplace transform. How do I massage this fract

Or "long division". s divides into 2s twice. 2 times s+ 6 is 2s+ 12 and subtracting: (2s+ 0)- (2s+ 12)= -12. s+ 6 divides into 2s twice with remainder -12:

.

Re: Getting stuck on a simple inverse Laplace transform. How do I massage this fract

Quote:

Originally Posted by

**BAdhi**
you can get it like this easily,

Yup, I was right. Kicking myself. This part of Laplace transforms is an art. Dammit. :)

Thanks for showing me what I was missing. :)