Question 161147
Vertical asymptotes correspond to the zeroes of the denominator of a rational function.
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Since your function was:
{{{ g(x) = (x-3)/(x^2 - 1) }}}
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To find the asymptotes, set the denominator to zero and solve:
x^2 - 1 = 0
x^2 = 1
x = {-1, 1}
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Therefore, your "vertical asymptotes" are at
x=-1 and x=1