Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(x^2+4x+2)/(x^2-2x)`?

Answer 1

The function has non-removable discontinuities at `0` and `2`. It has no other discontinuities.

Explanation:

The function is undefined for `x=0` and for `x=2`, so it has discontinuities only at those two numbers. (Rational functions are continuous on their domains, so `f`.)

`lim_(xrarr0)f(x)` and `lim_(xrarr2)f(x)` do not exist, so te discontinuities cannot be removed.