Module 4: Rational Equations and Rational Functions

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 4.2 Textbook:  Graphs of Rational Functions

Learning Objectives

• Compare graphs of inverse variation equations.
• Graph rational functions.
• Solve real-world problems using rational functions.

Section 4.3 Textbook:  Division of Polynomials

Learning Objectives

• Divide a polynomials by a monomial.
• Divide a polynomial by a binomial.
• Rewrite and graph rational functions.

Section 4.4 Textbook:  Rational Expressions

Learning Objectives

• Simplify rational expressions.
• Find excluded values of rational expressions.
• Simplify rational models of real-world situations.

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 4.6 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.

Video Lessons

1. Adding and Subtracting Rational Expressions

Video Examples

1. Ex 1:  Add and Subtract Rational Expressions - Like Denominators
2. Ex 2:  Add and Subtract Rational Expressions - Like Denominators
3. Ex 3:  Add and Subtract Rational Expressions - Like Denominators
4. Ex:  Add and Subtract Rational Expressions - Opposite Denominators
5. Ex 1:  Add and Subtract Rational Expressions - Unlike Denominators
6. Ex 2:  Add and Subtract Rational Expressions - Unlike Denominators
7. Ex 3:  Add and Subtract Rational Expressions - Unlike Denominators
8. Ex 4:  Add and Subtract Rational Expressions - Unlike Denominators

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.

Video Lessons

1. Solving Rational Equations
2. Rational Equation Applications I
3. Rational Equation Applications II

Video Examples

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