# Module 4: Rational Equations and Rational Functions

**Section 4.1 Textbook: Inverse Variation Models**

Section 4.1 Textbook: Inverse Variation Models

**Learning Objectives**

• Distinguish direct and inverse variation.

• Graph inverse variation equations.

• Write inverse variation equations.

• Solve real-world problems using inverse variation equations.

**Section 4.1 Videos**

**Section 4.2 Textbook: Graphs of Rational Functions**

Section 4.2 Textbook: Graphs of Rational Functions

**Learning Objectives**

• Compare graphs of inverse variation equations.

• Graph rational functions.

• Solve real-world problems using rational functions.

**Section 4.2 Videos**

**Video Lessons**

- Ex 1: Graphing Rational Functions
- Ex 2: Graphing Rational Functions
- Graphing Rational Functions
- Determining Vertical and Horizontal Asymptotes of Rational Functions
- Determining Slant Asymptotes of Rational Functions

**Video Examples**

- Ex: The Domain of Rational Functions
- Ex 3: Graphing Rational Functions
- Ex 4: Graphing Rational Functions
- Ex 5: Graphing Rational Functions
- Ex 6: Graphing Rational Functions

**Section 4.3 Textbook: Division of Polynomials**

Section 4.3 Textbook: Division of Polynomials

**Learning Objectives**

• Divide a polynomials by a monomial.

• Divide a polynomial by a binomial.

• Rewrite and graph rational functions.

**Section 4.3 Videos**

**Video Lessons**

- Dividing Polynomials by a Monomial
- Dividing Polynomials – Long Division
- Dividing Polynomials – Synthetic Division

**Video Examples**

- Ex: Divide a Polynomial by a Monomial
- Ex 1: Divide a Trinomial by a Binomial Using Long Division
- Ex 2: Divide a Trinomial by a Binomial Using Long Division
- Ex 3: Divide a Polynomial by a Binomial Using Long Division
- Ex 4: Divide a Polynomial by a Binomial Using Long Division
- Ex 5: Divide a Polynomial by a Binomial Using Long Division
- Ex 1: Divide a Trinomial by a Binomial Using Synthetic Division
- Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division
- Ex 3: Divide a Polynomial by a Binomial Using Synthetic Division
- Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division

**Section 4.4 Textbook: Rational Expressions**

Section 4.4 Textbook: Rational Expressions

**Learning Objectives**

• Simplify rational expressions.

• Find excluded values of rational expressions.

• Simplify rational models of real-world situations.

**Section 4.4 Videos**

**Section 4.5 Textbook: Multiplication and Division of Rational Expressions**

Section 4.5 Textbook: Multiplication and Division of Rational Expressions

**Learning Objectives**

• Multiply rational expressions involving monomials.

• Multiply rational expressions involving polynomials.

• Multiply a rational expression by a polynomial.

• Divide rational expressions involving polynomials.

• Divide a rational expression by a polynomial.

• Solve real-world problems involving multiplication and division of rational. expressions.

**Section 4.5 Videos**

**Video Lessons**

**Video Examples**

- Ex 1: Multiply Rational Expressions – Monomials
- Ex 2: Multiply Rational Expressions
- Ex 3: Multiply Rational Expressions
- Ex 4: Multiply Rational Expressions
- Ex 1: Dividing Rational Expressions – Monomials
- Ex 2: Dividing Rational Expressions
- Ex 3: Dividing Rational Expressions

**Section 4.6 Textbook: Addition and Subtraction of Rational Expressions**

Section 4.6 Textbook: Addition and Subtraction of Rational Expressions

**Learning Objectives**

• Add and subtract rational expressions with the same denominator.

• Find the least common denominator of rational expressions.

• Add and subtract rational expressions with different denominators.

• Solve real-world problems involving addition and subtraction of rational expressions.

**Section 4.6 Videos**

**Video Lessons**

**Video Examples**

- Ex 1: Add and Subtract Rational Expressions - Like Denominators
- Ex 2: Add and Subtract Rational Expressions - Like Denominators
- Ex 3: Add and Subtract Rational Expressions - Like Denominators
- Ex: Add and Subtract Rational Expressions - Opposite Denominators
- Ex 1: Add and Subtract Rational Expressions - Unlike Denominators
- Ex 2: Add and Subtract Rational Expressions - Unlike Denominators
- Ex 3: Add and Subtract Rational Expressions - Unlike Denominators
- Ex 4: Add and Subtract Rational Expressions - Unlike Denominators

**Section 4.7 Textbook: Solutions of Rational Equations**

Section 4.7 Textbook: Solutions of Rational Equations

**Learning Objectives**

• Solve rational equations using cross products.

• Solve rational equations using lowest common denominators.

• Solve real-world problems with rational equations.

**Section 4.7 Videos**

**Video Lessons**

**Video Examples**

- Ex 1: Solving Rational Equations
- Ex 2: Solving Rational Equations
- Ex 3: Solving Rational Equations
- Ex 4: Solving Rational Equations
- Ex 5: Solving Rational Equations
- Ex: Solve a Rational Equation - Alternative Method
- Ex 1: Rational Equation Application - Painting Together
- Ex 2: Rational Equation Application - Fill a Pool with Drain Open
- Ex 3: Rational Equation Application - Plane and Car Travelling the Same Time
- Ex 4: Rational Equation Application - Two Bikers Riding Different Distances

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