Rational function/R/Continuous/Fact

Let ${}P,Q\in \mathbb {R} [X]$ be polynomials and let ${}U:={\left\{x\in \mathbb {R} \mid Q(x)\neq 0\right\}}$.

Then the

rational function

$U\longrightarrow \mathbb {R} ,x\longmapsto {\frac {P(x)}{Q(x)}},$

is

continuous.

Proof, Write another proof