1. Adding and Subtracting Rational Expressions

2. WARM UP QUIZ tomorrow!! Can you find… Holes
Vertical and Horizontal Asymptotes
Domain and Range
Simplest Expression
Multiplying and Dividing Rationals

3. Review of Multiplying
Multiply or Divide the following. Find Holes and Asymptotes. 2. .

4. Middle School Math: Can you:
When adding and subtracting fractions with common denominators, simply add or subtract the numerator.

5. Adding and Subtracting:
We do the same with Rational Expressions!
If the denominators are the same, Add or Subtract the numerator

6. Practice .

7. 9.5 Adding and Subtracting with Unlike Denominators

8. Can we add/subtract fractions with different denominators?
We must find the Least Common Multiple before adding/subtracting! Add or subtract the following: 1. 2.

9. Unlike Denominators
When adding/subtracting fractions that have unlike denominators, we first need to change one (or both) so that they have a common denominator.
We do this by finding the Least Common Multiple (LCM)

10. Least Common Multiple
The LCM of two numbers is the smallest integer that is divisible by both numbers. List out the multiples of each number: 7: 21:

11. LCM
Find the LCM of each pair of numbers
4, 5
3, 8
4, 12

12. Steps for Adding or Subtracting
Find the Least Common Denominator (aka LCM)
Change each denominator by multiplying the Bottom AND THE TOP.
Now add/subtract like before 

13. Finding LCM of variables
For Variables, Take the Largest Exponent! Find the LCM of: x4 and x x3 and x2 3x5 and 9x8

14. Adding and Subtracting Fractions With Unlike Denominators
Add or subtract the following

15. Finding LCM of Expressions
For Expressions LCM: Include ALL factors!!
Find the LCM of each:
3(x + 2) and 5(x – 2)
x(x + 4) and 3x2(x + 4)
(x2 + 2x - 8) and (x2 – 4)
7(x2 – 25) and 2(x2 + 7x + 10)

16. Add or Subtract the Following1.

17. Add or Subtract the Following1.

18. Add or Subtract the Following1.

19. Add or Subtract the Following1.

20. Complex Fractions
A complex fraction is a faction that has a fraction in its numerator or denominator.

21. Simplifying
To Simplify, convert the numerator and denominator into one term each by finding the common denominator. Then DIVIDE by doing Keep Change Flip!

22. Try Some!
Simplify

23. Homework
HW 4.7

24. Homework
HW 4.6