Simplify the rational function \(\frac{x^3 - x^2 - x + 1}{x^2 - 1}\)

Step 1 ：Factor the numerator and the denominator. The numerator \(x^3 - x^2 - x + 1\) can be factored into \((x - 1)(x^2 + 1)\), and the denominator \(x^2 - 1\) can be factored into \((x - 1)(x + 1)\)

Step 2 ：Now we have \(\frac{(x - 1)(x^2 + 1)}{(x - 1)(x + 1)}\)

Step 3 ：Cancel the common factor \((x - 1)\) from the numerator and the denominator

Step 4 ：Hence the simplified form of the given rational function is \(\frac{x^2 + 1}{x + 1}\)