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4 7 x+2 x-2 + 4x + 24 2 x² - 4

4 7 x+2 x-2 + 4x + 24 2 x² - 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The given expression is: \[ \frac{4}{x + 2} - \frac{7}{x - 2} + \frac{4x + 24}{x^2 - 4} \] **Explanation:** This expression involves the addition and subtraction of three different rational expressions. Here's a breakdown of each term: 1. \(\frac{4}{x + 2}\) - This fraction has a numerator of 4 and a denominator of \(x + 2\). 2. \(\frac{7}{x - 2}\) - This fraction has a numerator of 7 and a denominator of \(x - 2\). 3. \(\frac{4x + 24}{x^2 - 4}\) - This fraction has a numerator of \(4x + 24\) and a denominator of \(x^2 - 4\). Note that the denominator can be factored as \((x - 2)(x + 2)\). To combine these fractions, you would need to find a common denominator.
Transcribed Image Text:The given expression is: \[ \frac{4}{x + 2} - \frac{7}{x - 2} + \frac{4x + 24}{x^2 - 4} \] **Explanation:** This expression involves the addition and subtraction of three different rational expressions. Here's a breakdown of each term: 1. \(\frac{4}{x + 2}\) - This fraction has a numerator of 4 and a denominator of \(x + 2\). 2. \(\frac{7}{x - 2}\) - This fraction has a numerator of 7 and a denominator of \(x - 2\). 3. \(\frac{4x + 24}{x^2 - 4}\) - This fraction has a numerator of \(4x + 24\) and a denominator of \(x^2 - 4\). Note that the denominator can be factored as \((x - 2)(x + 2)\). To combine these fractions, you would need to find a common denominator.
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