## Simplifying the Expression: (x^4 - 1) / (x^2 - 1)

This expression involves polynomial division, and it can be simplified by factoring both the numerator and the denominator.

### Factoring the Expression

**1. Factoring the Numerator:**

- The numerator (x^4 - 1) is a difference of squares. We can factor it as: (x^2 + 1)(x^2 - 1)

**2. Factoring the Denominator:**

- The denominator (x^2 - 1) is also a difference of squares: (x + 1)(x - 1)

### Simplifying the Expression

Now, let's substitute these factored expressions back into the original expression:

((x^2 + 1)(x^2 - 1)) / ((x + 1)(x - 1))

Notice that (x^2 - 1) appears in both the numerator and denominator. We can cancel these terms out:

**(x^2 + 1) / (x + 1)**

### Restrictions

It's important to note that this simplified expression is **only valid** for values of x where the original denominator (x^2 - 1) is not equal to zero.

This means that **x cannot be equal to 1 or -1**.

### Conclusion

The simplified form of the expression (x^4 - 1) / (x^2 - 1) is **(x^2 + 1) / (x + 1)**, with the restriction that **x ≠ 1 or -1**.