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
Rational expression
![**Task: Add the Rational Expressions and Simplify**
**Problem:**
\[
\frac{18x - 1}{5x} + \frac{2x - 4}{5x}
\]
**Instructions:**
1. **Combine the Expressions**: Since both fractions have the same denominator, you can add the numerators directly.
2. **Expression After Addition**:
Combine the numerators: \((18x - 1) + (2x - 4)\)
Place them over the common denominator:
\[
\frac{18x - 1 + 2x - 4}{5x}
\]
3. **Simplify the Numerator**:
Combine like terms in the numerator:
\[
18x + 2x - 1 - 4 = 20x - 5
\]
4. **Final Simplified Expression**:
The simplified expression is:
\[
\frac{20x - 5}{5x}
\]
5. **Simplify Further**:
Factor out the greatest common factor (GCF) in the numerator:
\(20x - 5 = 5(4x - 1)\)
\[
\frac{5(4x - 1)}{5x} = \frac{4x - 1}{x}
\]
6. **Answer**:
\[
\frac{4x - 1}{x}
\]
To check your understanding, enter your final answer in the box provided and validate your solution by simplifying further if necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c693121-0c53-4461-96bf-03d77f2fd62b%2F390fda7d-1a97-4065-847f-edc24d1f6a66%2Fy0ftmbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Add the Rational Expressions and Simplify**
**Problem:**
\[
\frac{18x - 1}{5x} + \frac{2x - 4}{5x}
\]
**Instructions:**
1. **Combine the Expressions**: Since both fractions have the same denominator, you can add the numerators directly.
2. **Expression After Addition**:
Combine the numerators: \((18x - 1) + (2x - 4)\)
Place them over the common denominator:
\[
\frac{18x - 1 + 2x - 4}{5x}
\]
3. **Simplify the Numerator**:
Combine like terms in the numerator:
\[
18x + 2x - 1 - 4 = 20x - 5
\]
4. **Final Simplified Expression**:
The simplified expression is:
\[
\frac{20x - 5}{5x}
\]
5. **Simplify Further**:
Factor out the greatest common factor (GCF) in the numerator:
\(20x - 5 = 5(4x - 1)\)
\[
\frac{5(4x - 1)}{5x} = \frac{4x - 1}{x}
\]
6. **Answer**:
\[
\frac{4x - 1}{x}
\]
To check your understanding, enter your final answer in the box provided and validate your solution by simplifying further if necessary.
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Topic - Addition of Rational expressions
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