1. Multiplying and Dividing Rational Expressions
Section 12.2
Multiplying and Dividing Rational Expressions

2. Multiplying and Dividing Rational Expressions
Property of Multiplication of Rational Function
Property
If and are rational expressions and B and D are
nonzero, then
In words: To multiply two rational expressions, write the numerators as a product and write the denominator as a product.

3. Find the product . Simplify the result.
Multiplying and Dividing Rational Expressions
Multiply Rational Expressions
Example
Find the product Simplify the result.
Solution

4. Find the product . Simplify the result.
Multiplying and Dividing Rational Expressions
Multiply Rational Expressions
Example
Find the product Simplify
the result.
Solution

5. Multiplying and Dividing Rational Expressions
Multiply Rational Expressions
Process
To multiply two rational expressions,
1. Factor the numerators and the denominators.
Multiply by using the property , where
B and D are nonzero.
3. Simplify the result.

6. Let and Find an equation of the product function Find
Multiplying and Dividing Rational Expressions
Finding a Product Function
Example
Let and
Find an equation of the product function
Find
Solution

7. Multiplying and Dividing Rational Expressions
Finding a Product Function
Example
Solution Continued

8. Division of Rational Expressions
Property of Dividing Rational Expressions
Property
If and are rational expressions and B, C, and D
are nonzero, then
In words: To divide by a rational expression, multiply by its reciprocal.

9. Division of Rational Expressions
Property of Dividing Rational Expressions
Example
Find the quotient
Solution

10. Division of Rational Expressions
Property of Dividing Rational Expressions
Solution Continued
Example
To divide two rational expressions,
Write the quotient as a product by using property:
, where B, C, and D are nonzero.
2. Find the product.
3. Simplify.
Process

11. Division of Rational Expressions
Dividing Two Rational Expressions
Example
Find the quotient
Solution

12. Let Find an equation of the quotient function. Find
Division of Rational Expressions
Dividing Two Rational Expressions
Solution Continued
Let
Find an equation of the quotient function.
Find
Example

13. Division of Rational Expressions
Finding a Quotient Function
Solution
Find the quotient

14. Division of Rational Expressions
Finding a Quotient Function
Solution Continued
Solution
Find the quotient

15. Perform the indicated operations:
Division of Rational Expressions
Combining Three Rational Equations
Example
Perform the indicated operations:
Solution

16. Division of Rational Expressions
Combining Three Rational Equations
Solution Continued
Example