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Multiplying rational expressions is similar to multiplying fractions in arithmetic.

Procedure

To Multiply Rational Expressions

Step 1 Factor the numerators and denominators.

Step 2 Cancel all pairs of factors common to the numerators and denominators.

Step 3 Multiply the numerators, and then multiply the denominators.

Example 1

Simplify: Solution Step 1 Factor. Step 2 Cancel common factors. Step 3 Multiply.    The result is .

Note

In your final answer, you may leave the parentheses. Or, you may use the Distributive Property to remove them. So, may be written as .

Dividing rational expressions is similar to dividing fractions in arithmetic.

Procedure

To Divide Rational Expressions

Step 1 Invert the second rational expression and change ÷ to ·.

Step 2 Multiply.

Example 2

Simplify: Solution Step 1 Invert the second rational expression and change ÷ to ·. Step 2 Multiply. Factor. Cancel. Simplify.    Thus, the result is .

Note: can be written as Some rational expressions contain both multiplication and division. To simplify these expressions, we can begin by changing division to multiplication.

Example 3

Simplify: Solution First, convert the division to multiplication. Factor. Cancel pairs of common factors. Multiply.     The result is . 