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
![**Topic: Simplifying Algebraic Expressions**
In this example, we are given an algebraic expression to simplify:
\[ \frac{5}{4a} - \frac{4}{5a} \]
To simplify this expression, follow these steps:
1. **Find a common denominator**:
The denominators in this expression are \( 4a \) and \( 5a \). The least common denominator (LCD) is \( 20a \).
2. **Rewrite each fraction with the common denominator**:
- For \(\frac{5}{4a}\), multiply the numerator and the denominator by 5:
\[
\frac{5}{4a} = \frac{5 \cdot 5}{4a \cdot 5} = \frac{25}{20a}
\]
- For \(\frac{4}{5a}\), multiply the numerator and the denominator by 4:
\[
\frac{4}{5a} = \frac{4 \cdot 4}{5a \cdot 4} = \frac{16}{20a}
\]
3. **Subtract the fractions**:
With both fractions having the common denominator \(20a\), we can subtract the numerators:
\[
\frac{25}{20a} - \frac{16}{20a} = \frac{25 - 16}{20a} = \frac{9}{20a}
\]
Therefore, the simplified form of the expression is:
\[ \frac{9}{20a} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2Fc82799e0-288e-4ad8-be0b-4e37db4505f7%2Fxht117u_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Simplifying Algebraic Expressions**
In this example, we are given an algebraic expression to simplify:
\[ \frac{5}{4a} - \frac{4}{5a} \]
To simplify this expression, follow these steps:
1. **Find a common denominator**:
The denominators in this expression are \( 4a \) and \( 5a \). The least common denominator (LCD) is \( 20a \).
2. **Rewrite each fraction with the common denominator**:
- For \(\frac{5}{4a}\), multiply the numerator and the denominator by 5:
\[
\frac{5}{4a} = \frac{5 \cdot 5}{4a \cdot 5} = \frac{25}{20a}
\]
- For \(\frac{4}{5a}\), multiply the numerator and the denominator by 4:
\[
\frac{4}{5a} = \frac{4 \cdot 4}{5a \cdot 4} = \frac{16}{20a}
\]
3. **Subtract the fractions**:
With both fractions having the common denominator \(20a\), we can subtract the numerators:
\[
\frac{25}{20a} - \frac{16}{20a} = \frac{25 - 16}{20a} = \frac{9}{20a}
\]
Therefore, the simplified form of the expression is:
\[ \frac{9}{20a} \]
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