I understand how they did everything except the last step, from 1/(-s/(s+1)^2) to -(s+1)^2/s
Could someone clarify? Thanks.
Well...
Using the fact that $\displaystyle \frac{1}{\frac{u}{v}} = 1 \cdot \frac{v}{u} \Rightarrow \frac{1}{\frac{s}{(s+1)^2}} = 1 \cdot \frac{(s+1)^2}{s}$
That is, dividing a term by x is like multiplying it by $\displaystyle \frac{1}{x}$. In this example, our x is $\displaystyle -\frac{s}{(s+1)^2}$ and so our 1/x is $\displaystyle -\frac{(s+1)^2}{s}$