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  Resuelve numerador y denominador y luego divida. 

The given expression simplifies to:

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

This is the simplified form of the fraction after resolving both the numerator and denominator.

Would you like more details on how the simplification was done?

Here are 5 related questions for further exploration:
1. How would this expression behave as \( x \) approaches infinity?
2. Can this fraction be factored further in specific cases (e.g., for specific values of \( x \))?
3. What is the domain of this simplified expression?
4. How does this expression behave when \( x = 1 \) or \( x = -1 \)?
5. Can you graph the function \( \frac{x^2 - 1}{x^2 + 1} \) and analyze its properties?

**Tip**: When simplifying rational expressions, always look for common factors or patterns in both the numerator and the denominator!

Resuelve numerador y denominador y luego divida.

Learn how to simplify the rational expression \( \frac{x - \frac{1}{x}}{x + \frac{1}{x}} \). This solution walks through resolving both the numerator and denominator to arrive at the simplified form \( \frac{x^2 - 1}{x^2 + 1} \), using key algebraic concepts such as factoring and quadratic identities. Ideal for students in Grades 9-12.

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