I am a bit confused about vertical asympotes. These two examples show different ways of getting asympotes. If I was to follow the first example to get the second example's asympote, it would not work out. Which example is correct, or are they both?

1. 2x/x^2-1 becomes factored to equal: 2x/(x-1)(x+1). So the asympotes are -1 for the first parenthesis and 1 for the second. The asympote was found by taking the number beside the x.

2. x/x^2-2x-3 factors to x/(x-3)(x+1) The asympotes according to the algebra book are three and -1. They were found not by taking the number beside the x as in the previous example, but by adding the number that would equal zero in the place of the x.

Which method is correct?

Thanks for your help -Gina

2 answers

Those actually both use the same method, the one you described for the second example. x=(-1) makes (x+1) equal to zero, and x=1 makes (x-1) equal to zero.
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