The rational function is defined as the quotient of two polynomials. Can functions that are equal to rational functions also be called rational, because they have the same properties?
One concrete example I could come up with is: $$ f(x) = \frac{x+0^{|x|}}{x^2-1} \\ g(x) = \frac{x^2}{x^3-x} $$
To my understanding these two funtions are identical. So, is $f$ rational?
Edit: I assume that $0^0$ is undefined as well as $g(0)$ hence $x/x$ is undefined for $x=0$. Also found the error and fixed it.