Tricky Algebra question

Discussion in 'Math' started by Jess_88, Jun 3, 2011.

  1. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    Hey guys.
    I was wondering if someone could show me the working out (simplification) for these two equation. This isn't a homework question... just study. If more information is needed... let me know :)

    1)

    [​IMG]

    2)
    [​IMG]

    thanks guys :)
     
  2. jegues

    Well-Known Member

    Sep 13, 2010
    735
    43
    For 1,

    \frac{5}{s+2} = \left( \frac{s+1}{2s+1} \right)V_{o}

    \frac{ 5 \times (2s+1)}{(s+2)(s+1)} = V_{o}

    \Rightarrow \frac{10s+5}{(s+2)(s+1)} = V_{o}

    Or if you're confused by the first simplification,

    \frac{V_{o}}{2s+1} + \frac{V_{o}}{2 + \frac{1}{s}}

    = \left( \frac{1}{2s+1} + \frac{1}{\frac{2s+1}{s}} \right)V_{o}

    = \left( \frac{1}{2s+1} + \frac{s}{2s+1} \right)V_{o}

    = \left( \frac{s+1}{2s+1} \right)V_{o}

    If I have time later I will look through the 2nd one as well. (It's the same type of algebra, nothing difficult)
     
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  3. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    ah thats great!
    Yeah I understand its simple... I just haven't worked with such fractions in a long time.
    If you do have time to do the second one later that would be great.
    Thanks for the help :)
     
  4. BillO

    Well-Known Member

    Nov 24, 2008
    985
    136
    You need to take it in steps. First step is to eliminate the 2/S denominator by multiplying both the top and bottom of the second term with S/2

    Such that we have:

    \frac{3}{S} -Vo\ \  -\frac{1}{2}-\frac{SVo}{2}\ \  +\frac{4}{S}-Vo\ \ =\ \ 0

    Collecting the terms with Vo on one side we get

     2Vo+\frac{S}{2}Vo\ \ =\ \ \frac{7}{S} - \frac{1}{2}

    Multiplying both sides by 2 and simplifying:

    \Rightarrow\ \ \ \ Vo(4+S)\ \ =\ \ \frac{14-S}{S}

    \Rightarrow\ \ \ \ Vo\ \ =\ \ \frac{14-S}{S(S+4)}
     
    Last edited: Jun 3, 2011
    Jess_88 likes this.
  5. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    aaah! I got it!
     
  6. victorhugo289

    Member

    Aug 24, 2010
    49
    3
    I thought you had to solve for something in here, but this is a plug-in-the-values type of equation.
    Not much simplification, really.
    It's more like a formula. It is a formula...
     
    Last edited: Jun 3, 2011
  7. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    Its a Laplace transformation question. I need to arrange the equation in terms of Vo and use partial fraction to determine the Laplace transformation.
    :)
     
  8. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
    2,039
    287
    You "just" need to find the common abominator. :)
    Eric
     
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