## Factoring and Simplifying (x^3 - 1) / (x - 1)

The expression (x^3 - 1) / (x - 1) represents a rational function, where the numerator and denominator are both polynomials. We can simplify this expression by factoring and canceling common factors.

### Factoring the Numerator

The numerator (x^3 - 1) is a difference of cubes. We can factor it using the following formula:

**a³ - b³ = (a - b)(a² + ab + b²)**

In our case, a = x and b = 1. Applying the formula, we get:

x³ - 1 = (x - 1)(x² + x + 1)

### Simplifying the Expression

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

(x³ - 1) / (x - 1) = [(x - 1)(x² + x + 1)] / (x - 1)

Since (x - 1) appears in both the numerator and denominator, we can cancel them out (assuming x ≠ 1):

[(x - 1)(x² + x + 1)] / (x - 1) = **x² + x + 1**

### Conclusion

Therefore, the simplified form of (x³ - 1) / (x - 1) is **x² + x + 1**, provided that x ≠ 1.