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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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2287fe-b48c-4110-a15b-090b303d0b72%2Fd20e5d84-8ed0-4eca-b76b-45c9c3b49d6c%2F73v07uj_processed.jpeg&w=3840&q=75)
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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