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Graph of y=(x+1)/(x-1)

  1. Sep 10, 2005 #1
    Could anyone show me what the graph of y=(x+1)/(x-1) looks like?
     
  2. jcsd
  3. Sep 10, 2005 #2

    LeonhardEuler

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    Gold Member

    This should help:
    [tex]y=\frac{x+1}{x-1}[/tex]
    [tex]=\frac{(x-1)+2}{x-1}[/tex]
    [tex]=\frac{x-1}{x-1}+\frac{2}{x-1}[/tex]
    [tex]=1+\frac{2}{x-1}[/tex]
    So it is the graph of y=1/x, just multiplied by two, shifted up by one, and shifted to the left by one.
     
  4. Sep 10, 2005 #3
    Where does the +2 come from?
     
    Last edited: Sep 10, 2005
  5. Sep 10, 2005 #4

    LeonhardEuler

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    Gold Member

    [tex]x+1=x-1+1+1=(x-1)+2[/tex]
     
  6. Sep 10, 2005 #5
    oh right. Hehe, thanks.
     
  7. Sep 10, 2005 #6
    How would simplify y=(1+2x)/(1-x)
     
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