5a Add: 24b 11a 18b2 In Example 6, we saw that the LCD of these rational expressions is 72b². We will multiply each one by the appropriate form of 1 to build it into an equivalent rational expression with a denominator of 72b². Since the denominators are different, we cannot add these rational expressions in their present form. 5a 11a 5a 3b 11a * Build each rational expression. 24b 1862 24b 3b 1862 15ab 44a Multiply the numerators. Multiply the denominators. %3D 7262 7262 Add the numerators. Write the sum over the common denominator. The result does not simplify. 7262 _ 2y 40z³ 5x Add: 32z
5a Add: 24b 11a 18b2 In Example 6, we saw that the LCD of these rational expressions is 72b². We will multiply each one by the appropriate form of 1 to build it into an equivalent rational expression with a denominator of 72b². Since the denominators are different, we cannot add these rational expressions in their present form. 5a 11a 5a 3b 11a * Build each rational expression. 24b 1862 24b 3b 1862 15ab 44a Multiply the numerators. Multiply the denominators. %3D 7262 7262 Add the numerators. Write the sum over the common denominator. The result does not simplify. 7262 _ 2y 40z³ 5x Add: 32z
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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Concept explainers
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Topic Video
Question
![### Adding Rational Expressions
To add:
\[ \frac{5a}{24b} + \frac{11a}{18b^2} \]
In Example 6, we saw that the Least Common Denominator (LCD) of these rational expressions is \( 72b^2 \). We will multiply each one by the appropriate form of 1 to build it into an equivalent rational expression with a denominator of \( 72b^2 \).
Since the denominators are different, we cannot add these rational expressions in their present forms.
\[ \frac{5a}{24b} + \frac{11a}{18b^2} = \frac{5a}{24b} \cdot \frac{3b}{3b} + \frac{11a}{18b^2} \cdot \frac{4}{4} \]
#### Steps:
1. **Build each rational expression**:
- Multiply \(\frac{5a}{24b}\) by \(\frac{3b}{3b}\).
- Multiply \(\frac{11a}{18b^2}\) by \(\frac{4}{4}\).
2. **Result after multiplication**:
\[ \frac{15ab}{72b^2} + \frac{44a}{72b^2} \]
3. **Add the numerators**:
\[ \frac{15ab + 44a}{72b^2} \]
4. **Final answer**:
- The sum remains \(\frac{15ab + 44a}{72b^2}\). The result does not simplify further.
### Another Example: Adding Rational Expressions
To add:
\[ \frac{2y}{40x^3} + \frac{5x}{32z} \]
Note: In this example, you would similarly find the least common denominator (LCD) of the given rational expressions and perform the steps to reach a common denominator before adding the numerators. The steps would follow the same principles demonstrated above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc60d0879-bf1d-4600-af9d-cdd728ad041f%2Fbc1459cf-f784-4cb1-be42-7de67bbe8fc2%2Fr24k48i_processed.png&w=3840&q=75)
Transcribed Image Text:### Adding Rational Expressions
To add:
\[ \frac{5a}{24b} + \frac{11a}{18b^2} \]
In Example 6, we saw that the Least Common Denominator (LCD) of these rational expressions is \( 72b^2 \). We will multiply each one by the appropriate form of 1 to build it into an equivalent rational expression with a denominator of \( 72b^2 \).
Since the denominators are different, we cannot add these rational expressions in their present forms.
\[ \frac{5a}{24b} + \frac{11a}{18b^2} = \frac{5a}{24b} \cdot \frac{3b}{3b} + \frac{11a}{18b^2} \cdot \frac{4}{4} \]
#### Steps:
1. **Build each rational expression**:
- Multiply \(\frac{5a}{24b}\) by \(\frac{3b}{3b}\).
- Multiply \(\frac{11a}{18b^2}\) by \(\frac{4}{4}\).
2. **Result after multiplication**:
\[ \frac{15ab}{72b^2} + \frac{44a}{72b^2} \]
3. **Add the numerators**:
\[ \frac{15ab + 44a}{72b^2} \]
4. **Final answer**:
- The sum remains \(\frac{15ab + 44a}{72b^2}\). The result does not simplify further.
### Another Example: Adding Rational Expressions
To add:
\[ \frac{2y}{40x^3} + \frac{5x}{32z} \]
Note: In this example, you would similarly find the least common denominator (LCD) of the given rational expressions and perform the steps to reach a common denominator before adding the numerators. The steps would follow the same principles demonstrated above.
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