Solving Rational Equations and Inequalities Algebra 2 8
![Solving Rational Equations and Inequalities Algebra 2 8 -5 Solving Rational Equations and Inequalities Algebra 2 8 -5](https://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-1.jpg)
Solving Rational Equations and Inequalities Algebra 2 8 -5
![• Multiplying variables on both sides of an equal sign may introduce extraneous • Multiplying variables on both sides of an equal sign may introduce extraneous](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-2.jpg)
• Multiplying variables on both sides of an equal sign may introduce extraneous solutions. • Check for extraneous solutions by plugging into the original equation. Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-3.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-4.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-5.jpg)
Solving Rational Equations
![• If rational functions are added in an equation, use the LCD to • If rational functions are added in an equation, use the LCD to](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-6.jpg)
• If rational functions are added in an equation, use the LCD to multiply all terms and “clear” the fraction Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-7.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-8.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-9.jpg)
Solving Rational Equations
![](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-10.jpg)
![](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-11.jpg)
![Mowing Lawns Tim and Ashley mow lawns together. Tim working alone could complete the Mowing Lawns Tim and Ashley mow lawns together. Tim working alone could complete the](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-12.jpg)
Mowing Lawns Tim and Ashley mow lawns together. Tim working alone could complete the job in 4. 5 hours, and Ashley could complete it alone in 3. 7 hours. How long does it take to complete the job when they work together? In 1 hour, Tim could complete In 1 hour, Ashley could complete of the job. Solving Rational Equations
![In t hours, Tim could complete In t hours, Ashley could complete Part completed In t hours, Tim could complete In t hours, Ashley could complete Part completed](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-13.jpg)
In t hours, Tim could complete In t hours, Ashley could complete Part completed by Tim plus part completed by Ashley or of the job. equals entire job. 1 Solving Rational Equations
![Solve the equation. Original equation Multiply each side by 16. 65. Distributive Property Simplify. Solve the equation. Original equation Multiply each side by 16. 65. Distributive Property Simplify.](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-14.jpg)
Solve the equation. Original equation Multiply each side by 16. 65. Distributive Property Simplify. Solving Rational Equations
![Simplify. Divide each side by 8. 2. Answer: It would take them about 2 Simplify. Divide each side by 8. 2. Answer: It would take them about 2](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-15.jpg)
Simplify. Divide each side by 8. 2. Answer: It would take them about 2 hours working together. Solving Rational Equations
![Cleaning Libby and Nate clean together. Nate working alone could complete the job in Cleaning Libby and Nate clean together. Nate working alone could complete the job in](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-16.jpg)
Cleaning Libby and Nate clean together. Nate working alone could complete the job in 3 hours, and Libby could complete it alone in 5 hours. How long does it take to complete the job when they work together? about 2 hours Solving Rational Equations
![Swimming Lynne swims for 1 hour in a stream that has a current of Swimming Lynne swims for 1 hour in a stream that has a current of](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-17.jpg)
Swimming Lynne swims for 1 hour in a stream that has a current of 2 miles per hour. She leaves her dock and swims upstream for 3 miles and then back to her dock. What is her swimming speed in still water? about 6. 6 mph Solving Rational Equations
![Solve Step 1 Values that make the denominator equal to 0 are excluded from Solve Step 1 Values that make the denominator equal to 0 are excluded from](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-18.jpg)
Solve Step 1 Values that make the denominator equal to 0 are excluded from the denominator. For this inequality the excluded value is 0. Step 2 Solve the related equation. Related equation Solving Rational Equations
![Multiply each side by 9 s. Simplify. Add. Divide each side by 6. Solving Multiply each side by 9 s. Simplify. Add. Divide each side by 6. Solving](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-19.jpg)
Multiply each side by 9 s. Simplify. Add. Divide each side by 6. Solving Rational Equations
![Step 3 Draw vertical lines at the excluded value and at the solution to Step 3 Draw vertical lines at the excluded value and at the solution to](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-20.jpg)
Step 3 Draw vertical lines at the excluded value and at the solution to separate the number line into regions. Now test a sample value in each region to determine if the values in the region satisfy the inequality. Solving Rational Equations
![Test is a solution. Solving Rational Equations Test is a solution. Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-21.jpg)
Test is a solution. Solving Rational Equations
![Test is not a solution. Solving Rational Equations Test is not a solution. Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-22.jpg)
Test is not a solution. Solving Rational Equations
![Test is a solution. Solving Rational Equations Test is a solution. Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-23.jpg)
Test is a solution. Solving Rational Equations
![Answer: The solution Solving Rational Equations Answer: The solution Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-24.jpg)
Answer: The solution Solving Rational Equations
![Solve Answer: Solving Rational Equations Solve Answer: Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-25.jpg)
Solve Answer: Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-26.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-27.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-28.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-29.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-30.jpg)
Solving Rational Equations
![Solving Rational Equations Solving Rational Equations](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-31.jpg)
Solving Rational Equations
![• Pages 605 – 606 • 20 – 26 even, 38 – 42 • Pages 605 – 606 • 20 – 26 even, 38 – 42](http://slidetodoc.com/presentation_image_h/b9ef63e70efd56283171d6e6572dd4bc/image-32.jpg)
• Pages 605 – 606 • 20 – 26 even, 38 – 42 even, 48, 50 Homework
- Slides: 32