Answer
(a) rational
(b) not rational
(c) rational
Work Step by Step
(a) $\displaystyle \frac{3x}{x^{2}-1}$ is a rational expression because it is a ratio of two polynomials.
(b) $\displaystyle \frac{\sqrt{x+1}}{2x+3}$ is not a rational expression because the numerator $\sqrt{x+1}$ is not a polynomial.
(c) $\displaystyle \frac{x(x^{2}-1)}{x+3}=\frac{x^{3}-x}{x+3}$ is a rational expression because it simplifies to a ratio of two polynomials.
