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General Simplification of (1+x)/(1-x)

  1. Aug 20, 2013 #1
    I know that (1-x)/(1+x) is equivalent to (2/(x+1)) - 1 via 'hand waving' in my textbook but i cannot figure out the steps to arrive at this result. Suggestions??
     
  2. jcsd
  3. Aug 20, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    You can write 1-x as -x-1+2=-(x+1)+2 and simplify.
    That is a usual trick for fractions like yours.
     
  4. Aug 20, 2013 #3
    Neat Trick. Thanks!!!
     
  5. Aug 20, 2013 #4

    Mark44

    Staff: Mentor

    An alternate approach is to divide - x + 1 by x + 1 using polynomial long division. If you don't know this technique, you can search Wikipedia using the search string "polynomial long division". Doing this, you get -1 + 2/(x + 1).
     
  6. Aug 20, 2013 #5
    Yet another equivalent way to see this is to replace 1 by (1+x)/(1+x) and you now have a common denominator of 1 + x. Gathering terms in the numerator yields 1 - x.
     
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