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12.5: Multiplication and Division of Rational Expressions

Difficulty Level: At Grade Created by: CK-12
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Learning Objectives

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.

Error Troubleshooting

In Review Questions 9, 12, and 16, remind students to write the expression on the right as a fraction with denominator equal to \begin{align*}1\end{align*}, 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.

Notes/Highlights Having trouble? Report an issue.

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