1. Today:
Final Exam Review
Rational Expressions Review
Adding/Subtracting Rational Expressions
Solving Rational Equations
Complete Class Work 4.11/4.12
May 27, 2015

2. Current Grading System:
Khan Academy: 20%
Class Work: 20%
Tests: 40%
Final Exam: 10%
Notebook: 10%
100% 45.0%
‘Average’ Student
25%
71%
64%
Proposal:
A minimum score of 75% on both remaining tests
guarantees a passing grade of at least 63% (higher
if you’ve earned it) for the 4th quarter.
Even with perfect
scores on the
final exam &
notebook, the
‘average’ student
cannot pass the
4th quarter.

3. Final Exam Review: (June 9th )
x2 + x – 42 = 0

4. Final Exam Review: (June 9th )
Simplify the following expression:
(x + 2) + (x – 2)(2x + 1) (2x2 – 3x -2) + (x +2)
Solve: 2x2 – x – 4 = 0

5. Simplifying Rational Expressions &
Multiplying/Dividing
Simplify: 𝟗𝒙(𝒙 − 𝟖)
𝟗𝒙(𝒙 − 𝟔)
÷
𝒙 − 𝟖
𝟓
=
𝟗𝒙(𝒙 − 𝟖)
𝟗𝒙(𝒙 − 𝟔)
∙
𝟓
𝒙 − 𝟖
=
𝟗𝒙 𝒙 − 𝟖 𝟓
𝟗𝒙(𝒙 − 𝟔)(𝒙 − 𝟖)
𝟓
𝒙 − 𝟔

6. Adding and Subtracting Rational Expressions
with unlike Denominators
Find the LCD
18a3b3
5d - 20
(x + 4)(x + 1)2
(s + 2)(s - 2 )(s + 5)

7. (x + 1)(x – 2)
x – 3
x2 – x – 2
x – 3
LCD = (x – 3)
Adding Rational Expressions
with unlike Denominators

8. 2
5
3 6 2
x
x x x

 
 2x x 3 2x
 23x x


x
x
 
2
3
15
2
x
x x


3
3

Adding Rational Expressions
with unlike Denominators
Add:

9. .
2
5 2
2 8 4
x
x x x

  
  4 2x x

 
 4x 
  4 2x x 
 2x 
 2x 
  4 2x x

   
5 2 4
4 2
x x
x x
  
 
  
3 4
4 2
x
x x


 
Subtracting Rational Expressions
with unlike Denominators

10. Solving Rational Equations

11. Solving Rational Equations

12. Solving Rational Equations

13. Final Note:
All of today’s practice problems come from the
Algebra II workbook.

14. Solve the Rational Equation.
Solve: Restrictions : x = -9
Multiply by the LCM: 5(x + 9) Reduce to clear fractions
5x – 25 = 2x + 18
– 2x -2x .
3x – 25 = 18
+ 25 + 25
3x = 43
(1/3) 3x = (1/3) 43
x = 43
3
5 2
9 5



x
x

15. Class Work: Please Change #2 to the following

16. Adding and Subtracting Rational Expressions
with unlike Denominators
=
𝟐 𝒙+𝟔 +𝒙
(𝒙+𝟔)(𝒙−𝟑)
The LCD 𝐢𝐬 (𝐱 + 𝟔)(𝐱 − 𝟑)
𝟐
𝒙 − 𝟑
+
𝒙
𝒙 𝟐 + 𝟑𝒙 − 𝟏𝟖
𝟐
𝒙 − 𝟑
∙
𝒙 + 𝟔
𝒙 + 𝟔
+
𝒙
(𝒙 + 𝟔)(𝒙 − 𝟑)
=
𝟑𝒙+𝟏𝟐
(𝒙+𝟔)(𝒙−𝟑)