1. Types of Variation

2. How can we Identify an Inverse Variation? x241015 y 7.532

3. Examples Identify the following data sets as examples of direct or inverse variation, or neither. 3) x241015 y10831.5 x0.20.51.01.5 y8204060 x0.20.51.02.0 y40.168.04.0

4. Rational Functions

5. Examples

6. Multiplying Rational Expressions

7. Dividing Rational Expressions

8. Examples

9. Adding and Subtracting Rational Expressions First you need to get each expression to have the same denominator. Then add/subtract the numerators using the common denominator. It’s usually easiest to 1.simplify the original denominators so as to see any common factors they share. 2.Then multiply top and bottom of each expression by the factors not shared by their denominators until the denominators are the same. EXAMPLES FOLLOW

10. Examples

11. Simplifying Complex Fractions

12. Examples

13. How Can we Solve Rational Equations? A rational equation contains at least one rational expression. To solve it:  First, get rid of the denominators by multiplying through by their prime factors. This process can introduce extraneous solutions.  Next simplify and solve for the unknown.  Only solutions that obey original restrictions on the domain are allowable.  Finally, check for extraneous solutions by substituting your candidate solutions into the original equation.  OR: Graph both sides of the equation and use the INTERSECT function. You must still check the validity of the solutions.

14. Examples

15. More Examples

16. Solving Systems of Rational Equations

17. Examples

18. Solving Rational Inequalities 1)Write the inequality as an equation and solve it. 2)Find the forbidden values. 3)Use the values obtained from (1) and (2) to create intervals on a number line. 4)Then test points within each interval to see if the inequality condition is observed. Report the good intervals in the usual interval notation. OR GRAPH each side and choose the correct region.

19. Examples

20. Hwk 41 Pages 546-548: 19, 30, 32, 34, 37, 49, 50 Page 551: 14 Hwk 41 Pages 546-548: 19, 30, 32, 34, 37, 49, 50 Page 551: 14 Hwk 41 Pages 546-548: 19, 30, 32, 34, 37, 49, 50 Page 551: 14 Hwk 41 Pages 546-548: 19, 30, 32, 34, 37, 49, 50 Page 551: 14