# Easy simplification of a function

• October 15th 2009, 03:55 PM
Evan.Kimia
Easy simplification of a function
http://img337.imageshack.us/img337/7410/problem3b.jpg

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.
• October 15th 2009, 04:26 PM
Defunkt
Quote:

Originally Posted by Evan.Kimia
http://img337.imageshack.us/img337/7410/problem3b.jpg

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 $\frac{1}{\frac{u}{v}} = 1 \cdot \frac{v}{u} \Rightarrow \frac{1}{\frac{s}{(s+1)^2}} = 1 \cdot \frac{(s+1)^2}{s}$

That is, dividing a term by x is like multiplying it by $\frac{1}{x}$. In this example, our x is $-\frac{s}{(s+1)^2}$ and so our 1/x is $-\frac{(s+1)^2}{s}$
• October 15th 2009, 04:27 PM
skeeter
Quote:

Originally Posted by Evan.Kimia
http://img337.imageshack.us/img337/7410/problem3b.jpg

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?

$\frac{1}{a/b} = 1 \cdot \frac{b}{a} = \frac{b}{a}$
• October 15th 2009, 05:50 PM
Evan.Kimia
Thats what i thought, i wanted to be certain. Thanks!