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

1. brandon26

107
Could anyone show me what the graph of y=(x+1)/(x-1) looks like?

2. LeonhardEuler

863
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.

3. brandon26

107
Where does the +2 come from?

Last edited: Sep 10, 2005
4. LeonhardEuler

863
$$x+1=x-1+1+1=(x-1)+2$$

5. brandon26

107
oh right. Hehe, thanks.

6. brandon26

107
How would simplify y=(1+2x)/(1-x)