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Math Help - Request for further assistance with simplification of complex fraction.

  1. #1
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    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.

    Can someone please assist?

    Regards.
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  2. #2
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    \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  = \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?
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  3. #3
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    Not sure I can. It gets very ugly.

    Can you?

    Regards.
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  4. #4
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    I can

    maybe s+2 will cancel? ;D
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  5. #5
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    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?
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  6. #6
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    \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}
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  7. #7
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    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?
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