## Graphs

Could anyone show me what the graph of y=(x+1)/(x-1) looks like?

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 Recognitions: Gold Member This should help: $$y=\frac{x+1}{x-1}$$ $$=\frac{(x-1)+2}{x-1}$$ $$=\frac{x-1}{x-1}+\frac{2}{x-1}$$ $$=1+\frac{2}{x-1}$$ So it is the graph of y=1/x, just multiplied by two, shifted up by one, and shifted to the left by one.
 Where does the +2 come from?

Recognitions:
Gold Member

## Graphs

$$x+1=x-1+1+1=(x-1)+2$$

 oh right. Hehe, thanks.
 How would simplify y=(1+2x)/(1-x)
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