b) \( \frac{x^{3}-x}{x^{3}+2 x^{2}+x}= \)

To simplify the expression \( \frac{x^{3}-x}{x^{3}+2x^{2}+x} \), we can begin by factoring both the numerator and the denominator. In the numerator, \( x^{3} - x \) can be factored as \( x(x^{2} - 1) \), which further simplifies to \( x(x - 1)(x + 1) \). In the denominator, \( x^{3} + 2x^{2} + x \) can be factored by taking out a common factor of \( x \), yielding \( x(x^{2} + 2x + 1) \), which factors to \( x(x + 1)^{2} \). Now we can rewrite the original expression: \[ \frac{x(x - 1)(x + 1)}{x(x + 1)^{2}}. \] Provided \( x \neq 0 \), we can cancel out the common \( x \) in the numerator and denominator, leading us to: \[ \frac{(x - 1)(x + 1)}{(x + 1)^{2}}. \] Next, we can cancel out \( (x + 1) \) from the numerator and denominator (as long as \( x \neq -1 \)): \[ \frac{x - 1}{x + 1}. \] Thus, the simplified expression is: \[ \frac{x - 1}{x + 1}, \quad \text{for } x \neq 0 \text{ and } x \neq -1. \]