I read in Jaames E. Humphreys' book "Linear Algebraic Groups", that a rational function need not be regular.
Suppose that $X$ is a varity over an algebraically close field $K$. If I am not mistaken, a rational function over $X$ is a function in $K(X)$. And a function on $X$ is regular at a point $x \in X$ if there exists $g,h \in K[X]$, and an open subset $V \subseteq X$ containing $x$, such that for all $y \in V$, $h(y) \neq 0$ and $f(y) =g(y)/h(y)$. And $f(x)$ is a regular function if it is regular at every point in $X$.
I not understand why rational functions need not be regular, and I am wondering if there is any example of rational function being not regular.
Thank you very much~