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

$\displaystyle F(s) = \frac{2s}{s + 6}$

Now, I know the answer is $\displaystyle 2 \delta (t) - 12 e^{-6t} u(t)$

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:

$\displaystyle \frac{2s}{s + 6} = 2 - \frac{12}{s + 6}$

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