https://file.aiquickdraw.com/mathbot/file/1728934050159iltd8pcn.jpg

The problem asks to simplify the expression:

\[
\frac{x^2 - 25}{x^2 + 7x + 10}
\]

To solve this, let's follow these steps:

### Step 1: Factor the numerator and denominator.
- The numerator \( x^2 - 25 \) is a difference of squares and can be factored as:
  \[
  x^2 - 25 = (x - 5)(x + 5)
  \]

- The denominator \( x^2 + 7x + 10 \) is a quadratic trinomial that factors into two binomials:
  \[
  x^2 + 7x + 10 = (x + 5)(x + 2)
  \]

### Step 2: Simplify the expression.
The expression becomes:
\[
\frac{(x - 5)(x + 5)}{(x + 5)(x + 2)}
\]

Now, cancel out the common factor \( (x + 5) \), assuming \( x \neq -5 \) to avoid division by zero:
\[
\frac{x - 5}{x + 2}
\]

### Step 3: Identify the correct answer.
The simplified form is \( \frac{x - 5}{x + 2} \), which corresponds to option **A**.

### Final Answer: A. \(\frac{x - 5}{x + 2}\)

Would you like a detailed explanation or have any questions?

Here are five related questions to deepen your understanding:
1. How do you factor quadratic trinomials in general?
2. What is the difference of squares, and when can it be used?
3. Why is it important to consider restrictions like \( x \neq -5 \)?
4. How can you check if your factorization is correct?
5. How would the problem change if the quadratic in the denominator did not factor easily?

**Tip:** Always look for common factors between the numerator and denominator before simplifying.

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 the numerator and denominator. The solution involves key algebraic concepts, including the difference of squares and factoring quadratic trinomials. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation