Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Problem:** Divide the following expression and simplify your answer: \[ \frac{c+6}{c-4} + \frac{c-7}{c+8} \] **Solution Steps:** 1. **Find a common denominator:** - The denominators are \( (c-4) \) and \( (c+8) \). - The common denominator is \( (c-4)(c+8) \). 2. **Rewrite each fraction with the common denominator:** - The first fraction becomes \(\frac{(c+6)(c+8)}{(c-4)(c+8)}\). - The second fraction becomes \(\frac{(c-7)(c-4)}{(c-4)(c+8)}\). 3. **Combine the fractions:** - Add the numerators: \((c+6)(c+8) + (c-7)(c-4)\). - Place the sum over the common denominator: \[ \frac{(c+6)(c+8) + (c-7)(c-4)}{(c-4)(c+8)} \] 4. **Simplify the numerator:** - Expand and collect like terms. 5. **Simplify the final expression if possible:** Finally, label your answer clearly in the box provided. **Note:** Please ensure all calculations are correct and the final expression is simplified as much as possible.
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Transcribed Image Text:**Problem:** Divide the following expression and simplify your answer: \[ \frac{c+6}{c-4} + \frac{c-7}{c+8} \] **Solution Steps:** 1. **Find a common denominator:** - The denominators are \( (c-4) \) and \( (c+8) \). - The common denominator is \( (c-4)(c+8) \). 2. **Rewrite each fraction with the common denominator:** - The first fraction becomes \(\frac{(c+6)(c+8)}{(c-4)(c+8)}\). - The second fraction becomes \(\frac{(c-7)(c-4)}{(c-4)(c+8)}\). 3. **Combine the fractions:** - Add the numerators: \((c+6)(c+8) + (c-7)(c-4)\). - Place the sum over the common denominator: \[ \frac{(c+6)(c+8) + (c-7)(c-4)}{(c-4)(c+8)} \] 4. **Simplify the numerator:** - Expand and collect like terms. 5. **Simplify the final expression if possible:** Finally, label your answer clearly in the box provided. **Note:** Please ensure all calculations are correct and the final expression is simplified as much as possible.
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