2 min read Jun 17, 2024

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


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.

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