The given expression is:

\[
\frac{\frac{x^2 - 1}{x - y}}{\frac{x^2}{x - y}}
\]

To simplify this, follow these steps:

### Step 1: Cancel the common denominator.
Both the numerator and denominator have the factor \( \frac{1}{x - y} \), so we can cancel that out:

\[
\frac{x^2 - 1}{x^2}
\]

### Step 2: Factor the numerator \( x^2 - 1 \).
The numerator is a difference of squares, so we can factor it as:

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

### Step 3: Write the final simplified expression.
Thus, the simplified expression is:

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

This is the most simplified form of the original expression.

Would you like to see more details or ask any questions?

Here are 5 related questions:
1. What are the steps to simplify complex rational expressions?
2. How do you recognize and factor a difference of squares?
3. How can you simplify expressions involving variables in the denominator?
4. What are some common mistakes to avoid when canceling terms in rational expressions?
5. How does the distributive property help in simplifying rational expressions?

**Tip**: Always check if terms in the numerator and denominator can be factored or canceled to simplify expressions faster.

Learn how to simplify the rational expression ((x^2 - 1)/(x - y)) / (x^2/(x - y)) step-by-step. This solution involves key algebraic concepts like factoring a difference of squares and canceling common terms in rational expressions. Suitable for students in Grades 9-11.

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