At the end of this lesson, students will be able to:
- 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.
Teaching Strategies and Tips
Use the ordinary fractions in Example 1 to motivate multiplying and dividing variable rational expressions.
Use Example 2 to point out that an answer can be more readily obtained by reducing common factors before multiplying.
- Suggest students to factor all polynomial expressions as much as possible first.
In Review Questions 9, 12, and 16, remind students to write the expression on the right as a fraction with denominator equal to 1, and then proceed to multiply or divide.
General Tip: Remind students to rewrite division problems as multiplication problems.
General Tip: In a division problem, some students will invert the first fraction. Remind students to invert the second.