1. 8.5: Adding and Subtracting Rational Expressions
Worksheet Key
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8.5: Adding and Subtracting Rational Expressions

2. 8.5: Adding and Subtracting Rational Expressions
Page 577 3) B 4) A 5) C 7) 9)
11)
13)
15)
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19)
Must factor first
21)
25)
27)
29)
31)
(x + 2)(x + 7)
33)
35)
37)
39)
41)
43)
EP1)
–(x + 7)
EP2)
–(x + 3)
EP3)
(x2 + 5x + 25)(2x – 1)
EP4)
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8.5: Adding and Subtracting Rational Expressions

3. Adding & Subtracting Rational Expressions
Section 8.5
Adding & Subtracting Rational Expressions
8.5: Adding and Subtracting Rational Expressions
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4. 8.5: Adding and Subtracting Rational Expressions
Review
Add (2/3) + (6/3)
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8.5: Adding and Subtracting Rational Expressions

5. 8.5: Adding and Subtracting Rational Expressions
Example 1
Add
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8.5: Adding and Subtracting Rational Expressions

6. 8.5: Adding and Subtracting Rational Expressions
Example 2
Subtract
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8.5: Adding and Subtracting Rational Expressions

7. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Subtract
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8.5: Adding and Subtracting Rational Expressions

8. Steps of Add & Subtract Rational Expressions
When given an equation, rewrite the fraction using the common denominator.
Simplify by combining like terms of both the numerator and denominator.
Multiply if needed and then simplify.
Reduce to lowest terms up top. Do NOT distribute the bottom.
Determine what values the variables cannot equal to.
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8.5: Adding and Subtracting Rational Expressions

9. Steps of Add & Subtract Rational Expressions
Common
Denominator
Multiply
Divide
Cancel
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8.4: Multiply and Divide Rational Expressions

10. 8.5: Adding and Subtracting Rational Expressions
Review
What is the common denominator of 6 and 15?
What is the common denominator of 3x and 9x2?
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8.5: Adding and Subtracting Rational Expressions

11. 8.5: Adding and Subtracting Rational Expressions
Review
Simplify (2/3) – (1/2)
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8.5: Adding and Subtracting Rational Expressions

12. 8.5: Adding and Subtracting Rational Expressions
Example 3
Find the LCD of (x + 2) and (x – 2)
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8.5: Adding and Subtracting Rational Expressions

13. 8.5: Adding and Subtracting Rational Expressions
Example 4
Find the LCD of t2 – t – 6 and t2 + 3t + 2
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8.5: Adding and Subtracting Rational Expressions

14. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Find the LCD of (x – 4)2 and (3x – 12)
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8.5: Adding and Subtracting Rational Expressions

15. 8.5: Adding and Subtracting Rational Expressions
Example 5
Solve and identify any x-values for which the expression is/are undefined.
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8.5: Adding and Subtracting Rational Expressions

16. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Solve and identify any x-values for which the expression is/are undefined.
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8.5: Adding and Subtracting Rational Expressions

17. 8.5: Adding and Subtracting Rational Expressions
Example 6
Simplify (7/6x) – (5/8x)
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8.5: Adding and Subtracting Rational Expressions

18. 8.5: Adding and Subtracting Rational Expressions
Example 7
Simplify and define what x values is/are undefined
What is the common denominator?
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8.5: Adding and Subtracting Rational Expressions

19. 8.5: Adding and Subtracting Rational Expressions
Example 7
Simplify and define what x values is/are undefined
Apply the missing factors to the numerator.
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8.5: Adding and Subtracting Rational Expressions

20. 8.5: Adding and Subtracting Rational Expressions
Example 7
Simplify and define what x values is/are undefined
Simplify. Distribute the top.
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8.5: Adding and Subtracting Rational Expressions

21. 8.5: Adding and Subtracting Rational Expressions
Example 7
Simplify and define what x values is/are undefined
Combine like terms.
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8.5: Adding and Subtracting Rational Expressions

22. 8.5: Adding and Subtracting Rational Expressions
Example 7
Simplify and define what x values is/are undefined
Define what x values is/are undefined
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8.5: Adding and Subtracting Rational Expressions

23. 8.5: Adding and Subtracting Rational Expressions
Example 8
Simplify and define what x values is/are undefined
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8.5: Adding and Subtracting Rational Expressions

24. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Simplify and define what x values is/are undefined
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8.5: Adding and Subtracting Rational Expressions

25. 8.5: Adding and Subtracting Rational Expressions
Example 9
Simplify and define what x values is/are undefined
What is the first step in factoring?
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8.5: Adding and Subtracting Rational Expressions

26. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Simplify and define what x values is/are undefined
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8.5: Adding and Subtracting Rational Expressions

27. 8.5: Adding and Subtracting Rational Expressions
Example 10
Simplify and define what x values is/are undefined
What is the first step in factoring?
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8.5: Adding and Subtracting Rational Expressions

28. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Simplify and define what x values is/are undefined
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8.5: Adding and Subtracting Rational Expressions

29. 8.5: Adding and Subtracting Rational Expressions
Example 11
Simplify and define what x values is/are undefined of (x + 2)–2 – (x2 – 4)–1
Rewrite the problem
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8.5: Adding and Subtracting Rational Expressions

30. 8.5: Adding and Subtracting Rational Expressions
Example 11
Simplify and define what x values is/are undefined of (x + 2)–2 – (x2 – 4)–1
Apply and Simplify
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8.5: Adding and Subtracting Rational Expressions

31. 8.5: Adding and Subtracting Rational Expressions
Your Turn
Simplify (x – y)–1 – (x + y)–1 and assume that all expressions are defined.
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8.5: Adding and Subtracting Rational Expressions

32. 8.5: Adding and Subtracting Rational Expressions
Assignment
Pg 586: 3-29 odd, 41
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8.5: Adding and Subtracting Rational Expressions