1. 9.5: Addition, Subtraction, and Complex Fractions Objectives: Students will be able to… Add and subtract rational expressions Simplify complex fractions

2. To add or subtract rational expressions you need a common denominator!!! O Example: 1. 2. Common Denominator…so just subtract numerators

3. You Try…Add or subtract

4. When you have unlike denominators, find the Least Common Denominator (LCD) of the rational expression. (May need to factor denominators first!!) O Rewrite each expression using the LCD O We do this with regular fractions LCD = 6

5. Now, lets do it with rational expressions: Factor denominators: This one needs a 2x +1 This one needs another x

6. Subtract. Factor Denominators: Needs an (x-3) Needs another (x+3)

7. You Try: Perform the indicated operation

8. Add or subtract.

9. Complex Fractions O A fraction within a fraction!! O Contains a fraction in numerator or denominator Example:

10. It is against the law to have a fraction within a fraction, so lets simplify: METHOD 1: Add expressions in denominator: Multiply by reciprocal, and simplify:

11. Method 2: Multiply numerator and denominator by LCD of both (don’t forget to distribute)

12. Simplify: