## Simplifying the Expression (x^2 - y^2) / (x - y)

The expression (x^2 - y^2) / (x - y) is a classic example of how to simplify algebraic expressions using factorization. Let's break down the process step-by-step:

### Understanding the Expression

**Numerator:**The numerator (x^2 - y^2) represents the difference of two squares.**Denominator:**The denominator (x - y) is a simple binomial.

### Factoring the Numerator

The difference of squares pattern tells us that:
**a^2 - b^2 = (a + b)(a - b)**

Applying this to our numerator:
**x^2 - y^2 = (x + y)(x - y)**

### Simplifying the Expression

Now we can rewrite the original expression as:

**(x + y)(x - y) / (x - y)**

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

**(x + y) / 1**

Which simplifies to:

**x + y**

### Conclusion

Therefore, the simplified form of (x^2 - y^2) / (x - y) is **x + y**, provided that x ≠ y (since the denominator cannot be zero). This simplification highlights the importance of recognizing common algebraic patterns and factoring expressions to achieve a more concise and manageable form.