Find inverse Laplace of . Book's answer (using partial fractions) . My answer (I have an extra 2 in the top of the second term).Where did my 2 go?

My work. Since my first term agrees with the book's answer, I'll just do inverse Laplace of

Now, to understand this I do it a little differently than is explained in the book (and various web pages).

If , then .

I want the inverse Laplace of F(s+1), but first I find the inverse L of F(s).

The Laplace of . Multiply both sides by and I get that the inverse Laplace of . Thus the inverseL of is .

But I want to find the inverse Laplace of which gives me , and I still have an extra 2 in the numerator.What'd I do wrong?