Prove that every rational function is continuous at every point in its domain.

(N/A) rational function $f$ is defined as $f(x) = \frac{p(x)}{q(x)}$,where $p(x)$ and $q(x)$ are polynomial functions and $q(x) \neq 0$.
The domain of $f$ is the set of all real numbers $x$ such that $q(x) \neq 0$.
We know that every polynomial function is continuous everywhere on the set of real numbers $\mathbb{R}$.
According to the algebra of continuous functions,if $p(x)$ and $q(x)$ are continuous functions,then their quotient $\frac{p(x)}{q(x)}$ is also continuous at all points where the denominator $q(x) \neq 0$.
Since $p(x)$ and $q(x)$ are polynomials,they are continuous everywhere. Therefore,the rational function $f(x) = \frac{p(x)}{q(x)}$ is continuous at every point in its domain.