Why x^2-4/x+2 in simplified form is not continuous?

    it is not continuous because is excluded from the original domain.the original definition of expression is  . inherently, you will divide by zero if you have  . so the domain is  .if we let  , applying the definition of continuity at -2 gets us    if the above is true, the function is continuous at -2. otherwise, discontinuous.since  is not defined, it will never be true; therefore it is discontinuous at . it is a removable discontinuity because  does exist.when you simplify something, you change how it looks, but you do not change the original definition, meanings, exclusions, etc. by doing that, you're pretty much defining a new expression; that is not simplifying.if you say that  with a domain of    is the same as  with a domain of  (no restrictions), then that is incorrect.  it is the same as  with a domain of  , hence why the simplified form is not continuous.