### Algebraic Expressions and Fractions In the following exercises, you will perform operations on algebraic fractions and express answers in simplified form. **Exercise 2** Perform the division operation on the given algebraic expressions: \[ \frac{13x^2}{20y^2} \div \frac{39x^2}{5y} \div \frac{2y^3}{26x^5y} \] **Exercise 3** Simplify the expression by dividing the polynomial fractions: \[ \frac{2a^2 - 11a + 12}{27 - 18a} \div \frac{a^3 + 4a^2}{6a^3 - 96a} \] **Exercise 4** Solve the division of the given expressions: \[ \frac{x^3 - 64}{x^3 + 64} \div \frac{x^2 - 16}{x^2 - 4x + 16} \] **Exercise 5** Divide and simplify the polynomial expressions: \[ \frac{8y^3 - 27}{64y^3 - 1} \div \frac{4y^2 - 9}{16y^2 + 4y + 1} \] **Exercise 6** Simplify the expression involving multiplication and division of fractions: \[ \frac{a^3 + b^3}{a^2 + 3ab + 2b^2} \cdot \frac{3a - 6b}{3a^2 - 3ab + 3b^2} \div \frac{a^2 - 4b^2}{a + 2b} \] --- ### Instructions 1. **Identify Common Factors**: Before performing operations, factorize the expressions to identify any common factors. 2. **Apply Operations**: Use appropriate arithmetic operations (multiplication, division) as indicated by the problems. 3. **Simplify**: Obtain the simplified fraction or algebraic expression by canceling out common factors. These exercises will help you deepen your understanding of polynomial fraction operations and enhance your simplification skills.
### Algebraic Expressions and Fractions In the following exercises, you will perform operations on algebraic fractions and express answers in simplified form. **Exercise 2** Perform the division operation on the given algebraic expressions: \[ \frac{13x^2}{20y^2} \div \frac{39x^2}{5y} \div \frac{2y^3}{26x^5y} \] **Exercise 3** Simplify the expression by dividing the polynomial fractions: \[ \frac{2a^2 - 11a + 12}{27 - 18a} \div \frac{a^3 + 4a^2}{6a^3 - 96a} \] **Exercise 4** Solve the division of the given expressions: \[ \frac{x^3 - 64}{x^3 + 64} \div \frac{x^2 - 16}{x^2 - 4x + 16} \] **Exercise 5** Divide and simplify the polynomial expressions: \[ \frac{8y^3 - 27}{64y^3 - 1} \div \frac{4y^2 - 9}{16y^2 + 4y + 1} \] **Exercise 6** Simplify the expression involving multiplication and division of fractions: \[ \frac{a^3 + b^3}{a^2 + 3ab + 2b^2} \cdot \frac{3a - 6b}{3a^2 - 3ab + 3b^2} \div \frac{a^2 - 4b^2}{a + 2b} \] --- ### Instructions 1. **Identify Common Factors**: Before performing operations, factorize the expressions to identify any common factors. 2. **Apply Operations**: Use appropriate arithmetic operations (multiplication, division) as indicated by the problems. 3. **Simplify**: Obtain the simplified fraction or algebraic expression by canceling out common factors. These exercises will help you deepen your understanding of polynomial fraction operations and enhance your simplification skills.
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
Answer all questions:
DIVISION of RATIONAL EXPRESSIONS
GENERAL DIRECTION: ALWAYS SHOW COMPLETE AND DETAILED SOLUTION. BOX YOUR FINAL ANSWER.
Find each quotient. Then, simplify your answer.
![### Algebraic Expressions and Fractions
In the following exercises, you will perform operations on algebraic fractions and express answers in simplified form.
**Exercise 2**
Perform the division operation on the given algebraic expressions:
\[
\frac{13x^2}{20y^2} \div \frac{39x^2}{5y} \div \frac{2y^3}{26x^5y}
\]
**Exercise 3**
Simplify the expression by dividing the polynomial fractions:
\[
\frac{2a^2 - 11a + 12}{27 - 18a} \div \frac{a^3 + 4a^2}{6a^3 - 96a}
\]
**Exercise 4**
Solve the division of the given expressions:
\[
\frac{x^3 - 64}{x^3 + 64} \div \frac{x^2 - 16}{x^2 - 4x + 16}
\]
**Exercise 5**
Divide and simplify the polynomial expressions:
\[
\frac{8y^3 - 27}{64y^3 - 1} \div \frac{4y^2 - 9}{16y^2 + 4y + 1}
\]
**Exercise 6**
Simplify the expression involving multiplication and division of fractions:
\[
\frac{a^3 + b^3}{a^2 + 3ab + 2b^2} \cdot \frac{3a - 6b}{3a^2 - 3ab + 3b^2} \div \frac{a^2 - 4b^2}{a + 2b}
\]
---
### Instructions
1. **Identify Common Factors**: Before performing operations, factorize the expressions to identify any common factors.
2. **Apply Operations**: Use appropriate arithmetic operations (multiplication, division) as indicated by the problems.
3. **Simplify**: Obtain the simplified fraction or algebraic expression by canceling out common factors.
These exercises will help you deepen your understanding of polynomial fraction operations and enhance your simplification skills.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbfefd57-6cd5-45bf-b890-c343c2fceb41%2F60fe9a97-9c55-4d8e-8037-e6cfe0a8ad1c%2Fylgnnx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Algebraic Expressions and Fractions
In the following exercises, you will perform operations on algebraic fractions and express answers in simplified form.
**Exercise 2**
Perform the division operation on the given algebraic expressions:
\[
\frac{13x^2}{20y^2} \div \frac{39x^2}{5y} \div \frac{2y^3}{26x^5y}
\]
**Exercise 3**
Simplify the expression by dividing the polynomial fractions:
\[
\frac{2a^2 - 11a + 12}{27 - 18a} \div \frac{a^3 + 4a^2}{6a^3 - 96a}
\]
**Exercise 4**
Solve the division of the given expressions:
\[
\frac{x^3 - 64}{x^3 + 64} \div \frac{x^2 - 16}{x^2 - 4x + 16}
\]
**Exercise 5**
Divide and simplify the polynomial expressions:
\[
\frac{8y^3 - 27}{64y^3 - 1} \div \frac{4y^2 - 9}{16y^2 + 4y + 1}
\]
**Exercise 6**
Simplify the expression involving multiplication and division of fractions:
\[
\frac{a^3 + b^3}{a^2 + 3ab + 2b^2} \cdot \frac{3a - 6b}{3a^2 - 3ab + 3b^2} \div \frac{a^2 - 4b^2}{a + 2b}
\]
---
### Instructions
1. **Identify Common Factors**: Before performing operations, factorize the expressions to identify any common factors.
2. **Apply Operations**: Use appropriate arithmetic operations (multiplication, division) as indicated by the problems.
3. **Simplify**: Obtain the simplified fraction or algebraic expression by canceling out common factors.
These exercises will help you deepen your understanding of polynomial fraction operations and enhance your simplification skills.
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