https://file.aiquickdraw.com/mathbot/file/1727056489102qxw94jxj.jpg

The problem given in the image is to simplify the following expression:

\[
\frac{x^2 - y^2}{(x - y)^2} \times \frac{1}{x + y}
\]

### Step-by-step simplification:

1. **Recognize that \( x^2 - y^2 \) is a difference of squares**:
   \[
   x^2 - y^2 = (x - y)(x + y)
   \]

   Now substitute this into the original expression:
   \[
   \frac{(x - y)(x + y)}{(x - y)^2} \times \frac{1}{x + y}
   \]

2. **Simplify the first fraction**:
   \[
   \frac{(x - y)(x + y)}{(x - y)^2} = \frac{x + y}{x - y}
   \]
   (since \( (x - y) \) cancels out from the numerator and denominator).

3. **Multiply the resulting expression by \( \frac{1}{x + y} \)**:
   \[
   \frac{x + y}{x - y} \times \frac{1}{x + y} = \frac{1}{x - y}
   \]

Thus, the simplified expression is:

\[
\boxed{\frac{1}{x - y}}
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Simplify \( \frac{x^2 - 9}{(x - 3)(x + 3)} \times \frac{1}{x + 3} \).
2. Simplify \( \frac{a^2 - b^2}{(a - b)^2} \times \frac{1}{a + b} \).
3. Simplify \( \frac{4x^2 - 25}{(2x - 5)^2} \times \frac{1}{2x + 5} \).
4. Simplify \( \frac{z^2 - 16}{(z - 4)(z + 4)} \times \frac{1}{z + 4} \).
5. Multiply and simplify \( \frac{x^3 - y^3}{(x - y)^3} \times \frac{1}{x + y} \).

### Tip:
When simplifying rational expressions, always look for common factors that can cancel out, especially for differences of squares, sums of cubes, or factorizable polynomials.

Simplify the expression: (x^2 - y^2) / (x - y)^2 × 1 / (x + y).

Learn how to simplify the rational expression (x^2 - y^2) / (x - y)^2 × 1 / (x + y) by factoring the difference of squares and simplifying the expression step by step. Suitable for high school students studying algebra and rational expressions.

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