Question

For what value of x is f(x)= (x-1)/((x^2)-1) discontinuous?

Why is it x=1 not x=-1?

Answer 1

I think both of them will make it discontinuous.
Note that x^2 - 1 must not be equal to zero, or else it will be discontinuous.
Since (-1)^2 - 1 = 0
and (1)^2 - 1 = 0

Answer 2

both are discontinuous; but they do not behave the same at each point

Answer 3

one is a hole, the other is an asymptote