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2. Rational Expressions
Chapter 8

3. 8 Rational Expressions 8.1 Simplifying Rational Expressions
8.2 Multiplying and Dividing Rational Expressions
8.3 Finding the Least Common Denominator
8.4 Adding and Subtracting Rational Expressions
Putting It All Together
8.5 Simplifying Complex Fractions
8.6 Solving Rational Equations
8.7 Applications of Rational Equations

4. 8.2 Multiplying and Dividing Rational Expressions Multiply Fractions
We multiply rational expressions the same way we multiply rational numbers. Multiply numerators, multiply denominators, and simplify.
Let’s review with multiplication of two fractions.
Multiply Fractions
Example 1
Solution
We can multiply numerators, multiply denominators, then simplify by dividing out common factors, or we can divide out the common factors before multiplying.
Factor and divide out common factors.
Multiply.
Simplify.

5. Multiply Rational Expressions
Example 2
Notice that
Solution
Factor and reduce.
Notice that was written as
so that you will be able to cancel out the term.
Multiply.

6. Example 3
Solution
Factor and reduce.
Multiply.

7. Example 4
Solution
Factor and reduce.
Multiply.

8. Divide Rational Expressions
When we divide rational numbers, we multiply by a reciprocal. For example,
.We divide rational expressions the same way. To divide
rational expressions, we multiply the first rational expression by the reciprocal of
the second rational expression. 2 1

9. Example 5 Solution 6 1 Get reciprocal.
Multiply by reciprocal and reduce. 1
Multiply.
Change division to
multiplication.

10. Example 6 Solution Get reciprocal. Multiply by reciprocal and reduce.
Change division to multiplication.
Multiply.

11. Example 7 Solution Multiply by reciprocal and reduce. Factor out a -1.

12. Example 8
Solution
Multiply by reciprocal
and reduce. 3 2
Multiply.