1. Warm up
Simplify without a calculator! 1) ) 1 4 − 7 8

2. Adding and Subtracting Rational Expressions
8.2

3. To add and subtract rational expressions, just like with fractions, you need a common denominator.
The common denominator is the LCM (Least Common Multiple) of the denominators

4. LCM of monomials
Example 1a:
Find the LCM of 15a2bc3 and 21b5c2

5. Example 1b: Find the LCD.
4𝑎 3𝑏 𝑐 3 , 15𝑏 12𝑎𝑐

6. LCM of polynomials x3 – x2 – 2x and x2 – 4x + 4
Example 2a: Find the LCM.
x3 – x2 – 2x and x2 – 4x + 4

7. Example 2b: Find the LCD.
3 𝑥 + 2 , 4𝑥 + 5 3𝑥 + 6

8. Example 2c: Find the LCD.
3 𝑥 2 −1 , 𝑥 + 5 4𝑥 −4

9. Example 3a
Simplify

10. Example 3b
Simplify
7 5 𝑥 2 𝑦 − 𝑥 10 𝑦 3

11. Example 3c
Simplify

12. Example 4
Simplify
7 6𝑥+12 − 𝑥 6𝑥−30

13. Example 5

14. Example 6
Simplify

15. Example 7
Simplify