$f(x)=\frac{x-1}{x^{2}-1}$

Step 1 ：Given function: \(f(x)=\frac{x-1}{x^{2}-1}\)

Step 2 ：Factor the denominator as a difference of squares: \(x^{2}-1 = (x-1)(x+1)\)

Step 3 ：Simplify the function by canceling out the common factors in the numerator and denominator: \(f(x)=\frac{x-1}{(x-1)(x+1)}\)

Step 4 ：Final Answer: \(\boxed{f(x) = \frac{1}{x + 1}}\)