Certainly! This text will appear on an educational website explaining equivalent expressions.---### Algebraic Expressions**Problem Statement:**Given $ x \ne -2 $, the expression $\frac{2x^2 + 5x + 8}{x + 2}$ is equivalent to:1. $ 2x^2 + \frac{9}{x + 2} $2. $ 2x + \frac{7}{x + 2} $ 3. $ 2x + 1 + \frac{6}{x + 2} $4. $ 2x + 9 - \frac{10}{x + 2} $**Solution Explanation:**To determine which of the given expressions is equivalent to $\frac{2x^2 + 5x + 8}{x + 2}$, you may need to perform polynomial long division or factor the numerator.Break down the steps for each of the choices by algebraic manipulation or by substituting values for $x$ and checking equality, keeping in mind the restriction $ x \ne -2 $.1. Option (1) checks if $\frac{2x^2 + 5x + 8}{x + 2}$ simplifies directly to $ 2x^2 + \frac{9}{x + 2} $.2. Option (2) checks if the expression simplifies to $ 2x + \frac{7}{x + 2} $.3. Option (3) checks if the expression simplifies to $ 2x + 1 + \frac{6}{x + 2} $.4. Option (4) checks if the expression simplifies to $ 2x + 9 - \frac{10}{x + 2} $.By comparing and simplifying, you'll be able to find which one matches the given algebraic expression.**Visual Aids:**No graphs or diagrams are provided with this problem.--- ### Additional Resources:- Guide on Polynomial Long Division- Worked Examples of Simplifying Rational Expressions

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Answered: 2x2 + 5x +8 Given x + -2, the…

2x2 + 5x +8 Given x + -2, the expression is equivalent to x +2 9 (1) 2x2 + x +2 6 (3) 2x + 1 + x +2 7 (2) 2x + x +2 10 (4) 2x + 9 x +2

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter9: Roots And Radicals

Section9.3: Add And Subtract Square Roots

Problem 232E: Explain the process for determining whether two radicals are like or unlike. Make sure your answer...

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Question

Certainly! This text will appear on an educational website explaining equivalent expressions.

---

### Algebraic Expressions

**Problem Statement:**
Given $ x \ne -2 $, the expression $\frac{2x^2 + 5x + 8}{x + 2}$ is equivalent to:

1. $ 2x^2 + \frac{9}{x + 2} $
2. $ 2x + \frac{7}{x + 2} $
3. $ 2x + 1 + \frac{6}{x + 2} $
4. $ 2x + 9 - \frac{10}{x + 2} $

**Solution Explanation:**
To determine which of the given expressions is equivalent to $\frac{2x^2 + 5x + 8}{x + 2}$, you may need to perform polynomial long division or factor the numerator.

Break down the steps for each of the choices by algebraic manipulation or by substituting values for $x$ and checking equality, keeping in mind the restriction $ x \ne -2 $.

1. Option (1) checks if $\frac{2x^2 + 5x + 8}{x + 2}$ simplifies directly to $ 2x^2 + \frac{9}{x + 2} $.
2. Option (2) checks if the expression simplifies to $ 2x + \frac{7}{x + 2} $.
3. Option (3) checks if the expression simplifies to $ 2x + 1 + \frac{6}{x + 2} $.
4. Option (4) checks if the expression simplifies to $ 2x + 9 - \frac{10}{x + 2} $.

By comparing and simplifying, you'll be able to find which one matches the given algebraic expression.

**Visual Aids:**
No graphs or diagrams are provided with this problem.

---

### Additional Resources:
- Guide on Polynomial Long Division
- Worked Examples of Simplifying Rational Expressions

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