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Find the least common denominator of 0 4x x+6 and X 1 6x S

Find the least common denominator of 0 4x x+6 and X 1 6x S

Algebra and Trigonometry (6th Edition)
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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**Rational Expressions: Finding the LCD of Rational Expressions with Linear Denominators** In this exercise, you are tasked with finding the least common denominator (LCD) of the following rational expressions: 1. \( \frac{4x}{x+6} \) 2. \( \frac{1}{6x} \) **Steps to Find the LCD:** 1. **Identify the Denominators:** - The denominators are \( x+6 \) and \( 6x \). 2. **Factor Each Denominator:** - \( x+6 \) is already in its simplest linear form. - \( 6x \) is also in simplest form, with a factor of 6. 3. **Determine the LCD:** - The LCD must include all unique factors from both denominators. - Combine \( (x+6) \) and \( 6x = 2 \cdot 3 \cdot x \). - The LCD is the product \( (x+6) \cdot 6x = 6x(x+6) \). Use this LCD for adding, subtracting, or comparing these rational expressions within the same equation or in operations. Ensure to multiply both numerator and denominator by any missing factors when transforming each fraction to have this common denominator.
Transcribed Image Text:**Rational Expressions: Finding the LCD of Rational Expressions with Linear Denominators** In this exercise, you are tasked with finding the least common denominator (LCD) of the following rational expressions: 1. \( \frac{4x}{x+6} \) 2. \( \frac{1}{6x} \) **Steps to Find the LCD:** 1. **Identify the Denominators:** - The denominators are \( x+6 \) and \( 6x \). 2. **Factor Each Denominator:** - \( x+6 \) is already in its simplest linear form. - \( 6x \) is also in simplest form, with a factor of 6. 3. **Determine the LCD:** - The LCD must include all unique factors from both denominators. - Combine \( (x+6) \) and \( 6x = 2 \cdot 3 \cdot x \). - The LCD is the product \( (x+6) \cdot 6x = 6x(x+6) \). Use this LCD for adding, subtracting, or comparing these rational expressions within the same equation or in operations. Ensure to multiply both numerator and denominator by any missing factors when transforming each fraction to have this common denominator.
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