Exercise 6, § 4

Show that every rational function $P(x)/Q(x)$ with coefficients in $\mathbf{R}$, defined at all points $x$ of $\mathbf{R}$ such that $Q(x) \neq 0$, can be extended by continuity to the points $+\infty$ and $-\infty$ (taking its values in $\overline{\mathbf{R}}$).