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# 12.5: Multiplication and Division of Rational Expressions

Difficulty Level: At Grade Created by: CK-12

## 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.

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## 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 $1$, 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.

Feb 22, 2012

Aug 22, 2014