Thread: Request for further assistance with simplification of complex fraction.

1. Request for further assistance with simplification of complex fraction.

Hello,

I have encountered another complex fraction that requires simplification:

K = [G(5s^2+10s+1)/(s+2)] / [1+(G/(s+2)]

Substitute in G=[5/(s^2-s+2.5)]

=> K = [5(5s^2+10s+1)] / [(s^2-s+2.5)(s+2)+5]
= [5(5s^2+10s+1)] / [(s^3+s^2+0.5s+10)]

This is proving rather difficult for me, and yet again I am sure once I see the solution I will wonder what all the fuss is about.

Regards.

2. $\displaystyle \displaystyle K = \frac{\frac{G(5s^2+10s+1)}{s+2}}{1+\frac{G}{s+2}} = \frac{\frac{G(5s^2+10s+1)}{s+2}}{\frac{s+2}{s+2}+\ frac{G}{s+2}}$

$\displaystyle \displaystyle = \frac{\frac{G(5s^2+10s+1)}{s+2}}{\frac{s+2+G}{s+2} } = \frac{G(5s^2+10s+1)}{s+2}\times \frac{s+2}{s+2+G}$

Can you finish it off?

3. Not sure I can. It gets very ugly.

Can you?

Regards.

4. I can

maybe s+2 will cancel? ;D

5. Ok - so I'm getting

=[G(5s^2+10s+1)/(s+2)] x [(s+2)/(s+2+G)]

=[(5/(s^2-s+2.5)x(5s^2+10s+1)/(s+2)] x [(s+2)/(s+2)+(5/(s^2-s+2.5)]

=[((10s^2+50s+5)/(s^2-s+2.5))/(s+2)] x [((s+2)/((s+2)(s^2-s+2.5)+5))/(s^2-s+2.5)]

As I said it gets ugly...

Any more tips?

6. $\displaystyle \displaystyle = \frac{G(5s^2+10s+1)}{s+2}\times \frac{s+2}{s+2+G}= \frac{G(5s^2+10s+1)}{s+2+G}$

7. So now I'm getting

= [5/(s^2-s+2.5))x(5s^2+10s+1)] / [s+2+(5/(s^2-s+2.5))]

= [(10s^2+50s+5) / (s^2-s+2.5)] / [(s+2(s^2-s+2.5)+5) / (s^2-s+2.5)]

= [(10s^2+50s+5)x(s^2-s+2.5)] / [(s+2(s^2-s+2.5)+5)x(s^2-s+2.5)]

= (10s^2+50s+5) / (s+2(s^2-s+2.5)+5)

Do you agree?