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To simplify the expression \(\frac{x^2 - 25}{x^2 + 7x + 10}\) to its lowest terms, we need to factor both the numerator and the denominator, then cancel any common factors.

1. **Factor the Numerator**:  
   The numerator is \(x^2 - 25\). This is a difference of squares, so we can factor it as:
   \[
   x^2 - 25 = (x - 5)(x + 5)
   \]

2. **Factor the Denominator**:  
   The denominator is \(x^2 + 7x + 10\). We need to find two numbers that multiply to \(10\) and add up to \(7\). These numbers are \(5\) and \(2\), so we can factor it as:
   \[
   x^2 + 7x + 10 = (x + 5)(x + 2)
   \]

3. **Simplify the Expression**:  
   Substitute the factors into the expression:
   \[
   \frac{x^2 - 25}{x^2 + 7x + 10} = \frac{(x - 5)(x + 5)}{(x + 5)(x + 2)}
   \]
   We can cancel the common factor \((x + 5)\) from the numerator and the denominator:
   \[
   = \frac{x - 5}{x + 2}
   \]

The simplified form of the expression is \(\frac{x - 5}{x + 2}\).

**Correct Answer: A. \(\frac{x - 5}{x + 2}\)**

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Would you like more details on factoring or simplification steps?

### Related Questions:
1. How do you factor a difference of squares?
2. How do you factor a trinomial like \(x^2 + 7x + 10\)?
3. What are common factorization techniques for simplifying fractions?
4. Can you simplify expressions without factoring?
5. How does canceling terms in fractions work in algebra?

### Tip:
Always check for factors in both the numerator and denominator before canceling terms to ensure you’re simplifying correctly.

Simplify \( \frac{x^2 - 25}{x^2 + 7x + 10} \) to lowest terms.

Learn how to simplify the rational expression \( \frac{x^2 - 25}{x^2 + 7x + 10} \) by factoring. This solution includes step-by-step guidance on factoring the difference of squares and trinomials. Ideal for students in Grades 8-10.

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