## Calculus (3rd Edition)

We can rewrite $f(x)$ as follows $$f(x)=x^2+\frac{3}{x}=\frac{x^3+3}{x}$$ which is a quotient of polynomials; that is, $f(x)$ is rational. Also, for $g(x)$, we have $$g(x)=3x^3-9x+\frac{1}{x^2}=\frac{3x^5-9x^3+1}{x^2}$$ which is a quotient of polynomials; that is, $g(x)$ is rational.