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To simplify \(\frac{x^2 - 25}{x^2 + 7x + 10}\) to its lowest terms, let's factor both the numerator and the denominator.

### Step 1: Factor the Numerator
The numerator is \(x^2 - 25\), which is a difference of squares:
\[
x^2 - 25 = (x + 5)(x - 5)
\]

### Step 2: Factor the Denominator
The denominator is \(x^2 + 7x + 10\), which factors into:
\[
x^2 + 7x + 10 = (x + 5)(x + 2)
\]

### Step 3: Simplify the Expression
Now we have:
\[
\frac{x^2 - 25}{x^2 + 7x + 10} = \frac{(x + 5)(x - 5)}{(x + 5)(x + 2)}
\]
We can cancel out the \((x + 5)\) term from the numerator and denominator:
\[
= \frac{x - 5}{x + 2}
\]

### Conclusion
The simplified form is \(\frac{x - 5}{x + 2}\).

### Answer
The correct answer is:
**A. \(\frac{x - 5}{x + 2}\)**

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Would you like more details on factoring or simplifying expressions?

Here are some related questions for further practice:
1. How do you factor expressions with a difference of squares?
2. How can you factor quadratic expressions like \(x^2 + 7x + 10\)?
3. What is the process for canceling terms in a rational expression?
4. How would the answer change if there were no common factors in the numerator and denominator?
5. What are the conditions where terms cannot be canceled in a fraction?

**Tip:** Always check for common factors when simplifying rational expressions.

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

Learn how to simplify the rational expression \( \frac{x^2 - 25}{x^2 + 7x + 10} \) to its lowest terms by factoring and canceling common factors. This solution involves understanding difference of squares and factoring quadratic trinomials, suitable for high school algebra students.

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