Problem
Determine if the function \( f(x) = \frac{x^2 + 2x + 1}{x^2 - 1} \) is a rational function.
Solution
Step 1 ：A rational function is any function which can be defined by a rational fraction, i.e., an algebraic fraction such that both the numerator and the denominator are polynomials.
Step 2 ：The numerator of the function \( f(x) = \frac{x^2 + 2x + 1}{x^2 - 1} \) is the polynomial \(x^2 + 2x + 1\), and the denominator is the polynomial \(x^2 - 1\).
Step 3 ：Therefore, the function \( f(x) = \frac{x^2 + 2x + 1}{x^2 - 1} \) is a rational function.
