## Simplifying the Expression (x^3 - 125) / (x - 5)

This expression represents a rational function, a fraction where both the numerator and denominator are polynomials. We can simplify this expression by using the difference of cubes factorization.

### Understanding the Difference of Cubes

The difference of cubes factorization states that:
**a³ - b³ = (a - b)(a² + ab + b²)**

In our expression, we have:

**a³ = x³****b³ = 125 = 5³**

### Applying the Factorization

Let's apply the difference of cubes factorization to the numerator:

(x³ - 125) = (x - 5)(x² + 5x + 25)

Now our expression becomes:

[(x - 5)(x² + 5x + 25)] / (x - 5)

### Cancellation and Final Result

Notice that we have a common factor of (x - 5) in both the numerator and denominator. We can cancel this factor, leaving us with:

**x² + 5x + 25**

Therefore, the simplified form of the expression (x³ - 125) / (x - 5) is **x² + 5x + 25**.

### Important Note

It's important to remember that this simplification is valid only when **x ≠ 5**. If x = 5, the denominator becomes zero, making the expression undefined.