$\frac{(3 x-1)(x+1)}{x^{2}-1} \div \frac{x}{x-1}$

Step 1 ：Rewrite the division as multiplication by the reciprocal: \(\frac{(3 x-1)(x+1)}{x^{2}-1} \cdot \frac{x-1}{x}\)

Step 2 ：Simplify the expression by canceling out common factors: \(\boxed{3 - \frac{1}{x}}\)