Question

How do you find the x values at which `f(x)=x/(x^2-1)` is not continuous, which of the discontinuities are removable?

Answer 1

See below.

Explanation:

This is a rational function.

Rational functions are continuous on their domains.

The domain of this `f` is all reals except `+-1`.

So `f` is discontinuous at `+-1`.

A discontinuity at `a` is removable if `lim_(xrarra)f(x)` exists. But the limit of `f` fails to exist for both `1` and `-1`. So neither discontinuity is removable.