Easy simplification of a function

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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!