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Solving rational equation
This document discusses solving rational equations and problems involving rational equations. It provides the procedure for solving rational equations which involves eliminating denominators by multiplying each term by the lowest common denominator. Examples are given to demonstrate solving rational equations and word problems involving setting up and solving rational equations. The document concludes with additional practice problems for the reader.
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Solving rational equation
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- 2. RATIONAL EQUATIONS › LEARNINGOUTCOMES: › Able to solve rational equations and solve problems involving rational equations.
- 3. PROCEDURE FOR SOLVINGRATIONAL EQUATIONS To solve rational equations: (a) Eliminate denominators by multiplying each term of the equation by the lcd. (b) Note that eliminating denominators may introduce extraneous solutions. Check the solutions of the transformed equations with the original equation.
- 4. SOLVING RATIONAL EQUATIONS Solvefor x: Example 1. 𝟐 𝒙 − 𝟑 𝟐𝒙 = 𝟏 𝟓 Example 2. 𝒙 𝒙+𝟐 − 𝟏 𝒙−𝟐 = 𝟖 𝒙 𝟐− 𝟒
- 5. PROBLEMS INVOLVING RATIONAL EQUATIONS Example3: In an inter-barangay basketball league. The team from Barangay Sto. NiÑo has won 12 out of 25 games, a winning percentage of 48%. How many games should they win in a row to improve their win percentage to 60%?
- 6. PROBLEMS INVOLVING RATIONAL EQUATIONS Example4: Rens walks 5 kilometers from his house to Quiapo to buy a new bike he uses to return home. He averaged 10 kilometers faster on his bike than on foot. If his total trip, took 1 hour and 20 minutes, what is his walking speed in kph? Use the formula 𝒗 = 𝒅 𝒕 .
- 7. Try this! Find thesolutions for each rational equation below. (a) 𝟑 𝒙+𝟏 = 𝟐 𝒙−𝟑 (b) 𝟐𝒙 𝒙+𝟏 + 𝟓 𝟐𝒙 = 𝟐 (c) You have 6 liters of a pineapple juice blend that is 50% pineapple juice. How many liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapple juice? Hint: If x is the amount of pure pineapple juice to be added, the percentage can be written as 𝟑+𝒙 𝟔+𝒙 .
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