Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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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Transcribed Image Text: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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