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Homework Help: Simplifying terms

  1. Nov 4, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm trying to simplify this polynomial
    ((s+1)/(2+s))/((s+1)+((s+1)/(s+2))(s+1))

    It's more readable if you view it here:
    http://www.wolframalpha.com/input/?i=((s+1)/(2+s))/((s+1)+((s+1)/(s+2))(s+1))

    It simplifies to 1/(2s+3)


    3. The attempt at a solution

    I'm not sure what steps are necessary to reduce it down to that.
     
  2. jcsd
  3. Nov 4, 2011 #2

    HallsofIvy

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    Science Advisor

    First, it's not a polynomial, it is a rational function.
    Is this it?
    [tex]\frac{\frac{s+1}{2+s}}{(s+1+ \frac{s+1}{s+2})(s+1)}[/tex]
    The first thing I would do is that addition in the denominator:
    [tex]s+1+ \frac{s+1}{s+2}= \frac{(s+1)(s+2)+ s+1}{s+2}[/tex]
    which we can then write as
    [tex](s+1)\frac{s+2+ 1}{s+2}= (s+1)\frac{s+3}{s+2}[/tex]

    With that,the full denominator is
    [tex](s+1)^2(1+ \frac{s+3}{s+2}= (s+1)^2\frac{2s+ 5}{s+2}[/tex]

    Also,dividing by a fraction is the same as multiplying by its reciprocal so the entire expression becomes
    [tex]\frac{s+1}{s+2}\frac{s+2}{(s+1)^2(2s+5)}[/tex]

    Can you finish that?
     
  4. Nov 4, 2011 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    No: the full denominator is just [tex](s+1)^2 \frac{s+3}{s+2} .[/tex]

    RGV
     
  5. Nov 4, 2011 #4
    According to the link the OP posted, the original "polynomial" is this:

    [tex]\frac{\frac{s+1}{2+s}}{(s+1)+\frac{s+1}{s+2}(s+1)}[/tex]


    I would start by multiplying by
    [tex]\frac{s+2}{s+2}[/tex]


    Also, note that the numerator can be restated as
    [tex]\frac{s+1}{s+2}[/tex]
    so that you have
    [tex]\frac{\frac{s+1}{s+2}}{(s+1)+\frac{s+1}{s+2}(s+1)}[/tex]
     
  6. Nov 4, 2011 #5
    sorry, my original equation might have been interpreted differently by wolfram. But the wolfram one is what I meant.

    how did you know to multiply by (s+2)/(s+2) zgozvrm?
     
  7. Nov 4, 2011 #6

    Mark44

    Staff: Mentor

    Because both the overall numerator and overall denominator had a denominator of s + 2. What zgozvrm actually did was multiply by 1 (which is always legal, since it doesn't change the value of what's being multiplied), in the form of (s + 2)/(s + 2).
     
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