# Thread: Easy simplification of a function

1. ## Easy simplification of a function

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.

2. Originally Posted by Evan.Kimia

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 $\displaystyle -\frac{(s+1)^2}{s}$

3. Originally Posted by Evan.Kimia

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.
remember how to divide by a fraction?

$\displaystyle \frac{1}{a/b} = 1 \cdot \frac{b}{a} = \frac{b}{a}$

4. Thats what i thought, i wanted to be certain. Thanks!