Monitor Projector

DrDelMath

Intermediate Algebra 5th Edition
by Elayn Martin-Gay
SUMMARY

Chapter 6: Rational Expressions

The essay named Fractions in the Special Topics section of this website should be used as a supplement to his chapter. The essay strongly emphasizes the connection of general rational expressions with familiar ordinary arithmetic fractions.

Section 6.1: Rational Functions and Multiplying and Dividing Rational Expressions

Textbook Objectives

1. Find the domain of a rational expression.

2. Simplify rational expressions.

3. Multiply rational expressions.

4. Divide rational expressions

Additional Goals

1. Know the definition of rational expression.

2. Know the definition of domain of a rational expression.

Minimal List of Exercises Page 347.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 14
Section 6.1 Exercise Set:13,15, 17, 21, 23, 27, 33, 35, 37, 43, 45, 47, 51,

 

Section 6.2: Adding and Subtracting Rational Expressions

Textbook Objectives

1. Add or subtract rational expressions with the same denominator.

2. Identify the least common denominator of two or more rational expressions.

3. Add or subtract rational expressions with different denominators.

Additional Goals

1. Know the definition of Least Common Denominator.

2. Be able to construct the opposite of a rational expression.

3. Use "Three Signs of a Fraction" to write multiple forms of a rational expression and its opposite.

Minimal List of Exercises Page 357.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 12
Section 6.2 Exercise Set:1 - 10, 11 - 22, 23 - 30, 31 - 36, 37 - 46, try 4 or 5 in the set 47 - 68, and then do at least 3 in the set 69 - 78.

 

Section 6.3: Simplifying Complex Fractions

Textbook Objectives

1. Simplify complex fractions by simplifying both numerator and denominator and then dividing.

2. Simplifying complex fractions by multiplying by a common denominator.

3. Simplify expressions with negative exponents.

Additional Goals

1. Recognize a complex fraction as an indication of ordinary division.

Minimal List of Exercises Page 364.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 8
Section 6.3 Exercise Set:1, 3, 7, 11, 15, 21, 27, 29, 31.

 

Section 6.4: Dividing Polynomials

Textbook Objectives

1. Divide a polynomial by a monomial.

2. Divide by a polynomial.

3. Use synthetic division to divide a polynomial by a binomial.

4. Use the remainder theorem to evaluate polynomials.

Additional Goals

2. Know the Division Algorithm for natural numbers.

2. Know the Division Algorithm for polynomials.

We studied this material much earlier--when we studied operations (addition, subtraction, multiplication, and division) of polynomials. Exercises are listed here for a bit of additional practice.

HERE are some examples of Long Division of Polynomials.

Minimal List of Exercises Page 373.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 6.4 Exercise Set:11, 13, 15, 17, 19, 21, 23, 28.

 

Section 6.6: Solving Equations Containing Rational Expressions

Textbook Objectives

1. Solve equations involving rational expressions.

Additional Goals

1. Know that multipling both sides of an equation does not necessarily produce an equivalent equation.

2. Know the definition of extraneous solution.

3. Know that checking possible solutions is an integral part of the process for solving equations involving rational expressions.

4. Know that the only proposed solutions which must be rejected are those which make some denominator 0 in the original equation.

Illustration to show that some, none, or all proposed solutions may be solutions. NEED TO CHECK.

Some general Examples about equations which will help you better understand the need to carefully consider proposed solutions and extraneous solutions.

Minimal List of Exercises Page 380.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Readiness Check: 1 - 12
Section 6.5 Exercise Set: 1, 3, 11, 12, 15, 17, 19, 20, 21.