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,...
Related questions
Question
![### Fraction Addition: Perform the Indicated Operation
#### Problem Statement
Perform the indicated operation:
\[
\frac{2}{8x+5} + 3
\]
#### Steps to Solve
1. **Express 3 as a Fraction**:
To add \(\frac{2}{8x+5}\) and 3, first express 3 as a fraction with a common denominator.
\[
3 = \frac{3(8x+5)}{8x+5} = \frac{24x + 15}{8x+5}
\]
2. **Add the Fractions**:
Now, add the two fractions:
\[
\frac{2}{8x+5} + \frac{24x + 15}{8x+5} = \frac{2 + 24x + 15}{8x+5}
\]
3. **Combine the Numerator**:
Combine like terms in the numerator:
\[
\frac{24x + 17}{8x+5}
\]
4. **Final Expression**:
The result of the operation is:
\[
\frac{24x + 17}{8x+5}
\]
Make sure to simplify your final result if possible. In this case, the fraction is already in its simplest form.
### Conclusion
You have successfully performed the indicated operation by expressing the constant as a fraction with a common denominator, adding the fractions, and simplifying the result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3be32d0d-85ce-4c7b-8211-afa0de24b46c%2Fabf49cae-80bf-44ed-89a2-817dc4dda664%2Fnuecsft_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Fraction Addition: Perform the Indicated Operation
#### Problem Statement
Perform the indicated operation:
\[
\frac{2}{8x+5} + 3
\]
#### Steps to Solve
1. **Express 3 as a Fraction**:
To add \(\frac{2}{8x+5}\) and 3, first express 3 as a fraction with a common denominator.
\[
3 = \frac{3(8x+5)}{8x+5} = \frac{24x + 15}{8x+5}
\]
2. **Add the Fractions**:
Now, add the two fractions:
\[
\frac{2}{8x+5} + \frac{24x + 15}{8x+5} = \frac{2 + 24x + 15}{8x+5}
\]
3. **Combine the Numerator**:
Combine like terms in the numerator:
\[
\frac{24x + 17}{8x+5}
\]
4. **Final Expression**:
The result of the operation is:
\[
\frac{24x + 17}{8x+5}
\]
Make sure to simplify your final result if possible. In this case, the fraction is already in its simplest form.
### Conclusion
You have successfully performed the indicated operation by expressing the constant as a fraction with a common denominator, adding the fractions, and simplifying the result.
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