1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    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

    User Avatar
    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).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simplifying terms
  1. Simplifying a fraction (Replies: 2)

Loading...