Example 1 Example 2 Example 3 Example 4
![Example 1 Example 2 Example 3 Example 4 Example 5 Solve a Rational Equation Example 1 Example 2 Example 3 Example 4 Example 5 Solve a Rational Equation](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-1.jpg)
![Solve Check your solution. The LCD for the three denominators is Original equation Multiply Solve Check your solution. The LCD for the three denominators is Original equation Multiply](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-2.jpg)
![6 1 1 1 Simplify. Add. 6 1 1 1 Simplify. Add.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-3.jpg)
![Check Original equation Simplify. The solution is correct. Check Original equation Simplify. The solution is correct.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-4.jpg)
![Answer: The solution is – 45. Answer: The solution is – 45.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-5.jpg)
![Solve Answer: Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-6.jpg)
![Solve Check your solution. The LCD is Original equation p– 1 1 Multiply by Solve Check your solution. The LCD is Original equation p– 1 1 Multiply by](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-7.jpg)
![Distributive Property Simplify. Add (2 p 2 – 2 p + 1) to each Distributive Property Simplify. Add (2 p 2 – 2 p + 1) to each](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-8.jpg)
![Divide each side by 3. Factor. or Zero Product Property Solve each equation. Divide each side by 3. Factor. or Zero Product Property Solve each equation.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-9.jpg)
![Check Original equation Simplify. Check Original equation Simplify.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-10.jpg)
![Original equation Simplify. Since p = – 1 results in a zero in the Original equation Simplify. Since p = – 1 results in a zero in the](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-11.jpg)
![Solve Answer: Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-12.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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-13.jpg)
![In t hours, Tim could complete or In t hours, Ashley could complete Part In t hours, Tim could complete or In t hours, Ashley could complete Part](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-14.jpg)
![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.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-15.jpg)
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-16.jpg)
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-17.jpg)
![Swimming Janine swims for 5 hours in a stream that has a current of Swimming Janine swims for 5 hours in a stream that has a current of](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-18.jpg)
![Time going with the current plus time going against the current equals total time. Time going with the current plus time going against the current equals total time.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-19.jpg)
![Multiply each side by r 2 – 1. r+1 r– 1 1 Distributive Property Multiply each side by r 2 – 1. r+1 r– 1 1 Distributive Property](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-20.jpg)
![Use the Quadratic Formula to solve for r. Quadratic Formula x = r, a Use the Quadratic Formula to solve for r. Quadratic Formula x = r, a](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-21.jpg)
![Simplify. Use a calculator. Answer: Since the speed must be positive, the answer is Simplify. Use a calculator. Answer: Since the speed must be positive, the answer is](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-22.jpg)
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-23.jpg)
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-24.jpg)
![Multiply each side by 9 s. Simplify. Add. Divide each side by 6. Multiply each side by 9 s. Simplify. Add. Divide each side by 6.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-25.jpg)
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-26.jpg)
![Test is a solution. Test is a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-27.jpg)
![Test is not a solution. Test is not a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-28.jpg)
![Test is a solution. Test is a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-29.jpg)
![Answer: The solution Answer: The solution](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-30.jpg)
![Solve Answer: Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-31.jpg)
![](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-32.jpg)
- Slides: 32
![Example 1 Example 2 Example 3 Example 4 Example 5 Solve a Rational Equation Example 1 Example 2 Example 3 Example 4 Example 5 Solve a Rational Equation](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-1.jpg)
Example 1 Example 2 Example 3 Example 4 Example 5 Solve a Rational Equation Elimination of a Possible Solution Work Problem Rate Problem Solve a Rational Inequality
![Solve Check your solution The LCD for the three denominators is Original equation Multiply Solve Check your solution. The LCD for the three denominators is Original equation Multiply](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-2.jpg)
Solve Check your solution. The LCD for the three denominators is Original equation Multiply each side by 24(3 – x).
![6 1 1 1 Simplify Add 6 1 1 1 Simplify. Add.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-3.jpg)
6 1 1 1 Simplify. Add.
![Check Original equation Simplify The solution is correct Check Original equation Simplify. The solution is correct.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-4.jpg)
Check Original equation Simplify. The solution is correct.
![Answer The solution is 45 Answer: The solution is – 45.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-5.jpg)
Answer: The solution is – 45.
![Solve Answer Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-6.jpg)
Solve Answer:
![Solve Check your solution The LCD is Original equation p 1 1 Multiply by Solve Check your solution. The LCD is Original equation p– 1 1 Multiply by](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-7.jpg)
Solve Check your solution. The LCD is Original equation p– 1 1 Multiply by the LCD, (p 2 – 1).
![Distributive Property Simplify Add 2 p 2 2 p 1 to each Distributive Property Simplify. Add (2 p 2 – 2 p + 1) to each](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-8.jpg)
Distributive Property Simplify. Add (2 p 2 – 2 p + 1) to each side.
![Divide each side by 3 Factor or Zero Product Property Solve each equation Divide each side by 3. Factor. or Zero Product Property Solve each equation.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-9.jpg)
Divide each side by 3. Factor. or Zero Product Property Solve each equation.
![Check Original equation Simplify Check Original equation Simplify.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-10.jpg)
Check Original equation Simplify.
![Original equation Simplify Since p 1 results in a zero in the Original equation Simplify. Since p = – 1 results in a zero in the](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-11.jpg)
Original equation Simplify. Since p = – 1 results in a zero in the denominator, eliminate – 1. Answer: The solution is p = 2.
![Solve Answer Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-12.jpg)
Solve Answer:
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-13.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.
![In t hours Tim could complete or In t hours Ashley could complete Part In t hours, Tim could complete or In t hours, Ashley could complete Part](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-14.jpg)
In t hours, Tim could complete or In t hours, Ashley could complete Part completed by Tim plus of the job. or part completed by Ashley equals of the job. entire job. 1
![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.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-15.jpg)
Solve the equation. Original equation Multiply each side by 16. 65. Distributive Property Simplify.
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-16.jpg)
Simplify. Divide each side by 8. 2. Answer: It would take them about 2 hours working together.
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-17.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? Answer: about 2 hours
![Swimming Janine swims for 5 hours in a stream that has a current of Swimming Janine swims for 5 hours in a stream that has a current of](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-18.jpg)
Swimming Janine swims for 5 hours in a stream that has a current of 1 mile per hour. She leaves her dock and swims upstream for 2 miles and then back to her dock. What is her swimming speed in still water? Words The formula that relates distance, time, and rate is Variables Let r be her speed in still water. Then her speed with the current is r + 1 and her speed against the current is r – 1.
![Time going with the current plus time going against the current equals total time Time going with the current plus time going against the current equals total time.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-19.jpg)
Time going with the current plus time going against the current equals total time. 5 Equation Solve the equation. Original equation
![Multiply each side by r 2 1 r1 r 1 1 Distributive Property Multiply each side by r 2 – 1. r+1 r– 1 1 Distributive Property](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-20.jpg)
Multiply each side by r 2 – 1. r+1 r– 1 1 Distributive Property 1 Simplify. Subtract 4 r from each side.
![Use the Quadratic Formula to solve for r Quadratic Formula x r a Use the Quadratic Formula to solve for r. Quadratic Formula x = r, a](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-21.jpg)
Use the Quadratic Formula to solve for r. Quadratic Formula x = r, a = 5, b = – 4, and c = – 5 Simplify.
![Simplify Use a calculator Answer Since the speed must be positive the answer is Simplify. Use a calculator. Answer: Since the speed must be positive, the answer is](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-22.jpg)
Simplify. Use a calculator. Answer: Since the speed must be positive, the answer is about 1. 5 miles per hour.
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-23.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? Answer: about 6. 6 mph
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-24.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
![Multiply each side by 9 s Simplify Add Divide each side by 6 Multiply each side by 9 s. Simplify. Add. Divide each side by 6.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-25.jpg)
Multiply each side by 9 s. Simplify. Add. Divide each side by 6.
![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](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-26.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.
![Test is a solution Test is a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-27.jpg)
Test is a solution.
![Test is not a solution Test is not a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-28.jpg)
Test is not a solution.
![Test is a solution Test is a solution.](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-29.jpg)
Test is a solution.
![Answer The solution Answer: The solution](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-30.jpg)
Answer: The solution
![Solve Answer Solve Answer:](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-31.jpg)
Solve Answer:
![](https://slidetodoc.com/presentation_image_h2/58b419e18da675fffd905dbedc8c81b7/image-32.jpg)
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