%2F(x-y).jpeg "(x^2-y^2)/(x-y)")
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.