# 12.5: Multiplication and Division of Rational Expressions

**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.

## Vocabulary

NONE

## 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*}

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.

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