1. Lesson 2-6

2. Warm-up You have 10 minutes to complete the half-sheet on multiplication and division of rational functions.

3. Refresher

4. Adding and Subtracting Rationals In order to add or subtract a rational, you must have a common denominator; that means finding the least common multiple of your denominators. If we already have a common denominator, we can add the numerators and simplify. Example: Add the following terms

5. Subtraction Example Subtract the following

6. Let’s Practice 1. 5. 2. 3. 4.

7. Least Common Multiple To find the least common multiple, we do the following: 1. Find the prime factorization of each number. 2. Find the common factors. 3. Multiply each number by the factors the other has that it does not. Example: Find the least common multiple of 6x and 8x 2.

8. Let’s Practice Find the LCM of the following 1. 6x and 9x 2. 4x and 18x 2 3. 12x 3 and 8 4. 25x 2 and 45x 5 5. 6x and 12x 6. 20x 2 and 30x 7. 10xyz and 15x 2 yz

9. Least Common Denominator We need to understand LCM to find the common denominator for rational expressions in order to add or subtract them. If the denominators have nothing in common, we multiply each term by the denominator of the other term. Example 1:Example 3: 11 + 15_ 12x 2 16x 5 Example 2:

10. Example 1

11. Example 2

12. Example 3

13. Let’s Practice 1. 2. 3.

14. Let’s Practice 4. 5. 6.