FocusOn...
Chapter
6
6.4RationalEquations
•identifyingnonpermissiblevaluesinarationalequation
•determiningthesolutiontoarationalequationalgebraically
•solvingproblemsusingarationalequation
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Solving Rational Equations: Identifying Non-Permissible Values and Determining Solutions, Exams of Algebra
Instructions on how to solve rational equations by identifying non-permissible values, determining the solution algebraically, and checking the solutions. It includes examples and exercises to practice. Rational equations are equations that contain at least one rational expression.
Typology: Exams
2021/2022
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Focus On ...
Chapter
6 6.4 Rational Equations
- identifying nonpermissible values in a rational equation
- determining the solution to a rational equation algebraically
- solving problems using a rational equation
Rational Equations
A rational equation is an equation that contains at least one rational expression.
Examples
To Solve a Rational Equation
- Factor^ each^ denominator^ and^ determine^ the^ least^ common^ denominator^ (LCD)
- Identify^ the^ nonpermissible^ values
- Multiply^ all^ terms^ on^ both^ sides^ of^ the^ equation^ by^ the^ LCD,^ and^ then^ simplify
- Solve^ for^ the^ variable
- Check^ that^ the^ solution(s)^ are^ permissible,^ and^ that^ they^ make^ sense^ in^ the^ given^ context
- Verify^ that^ any^ remaining^ solutions^ are^ correct^ in^ the^ original^ equation
Focus to clear the fraction
Example 1: Solving Rational Equations Solve the following equations. What values are nonpermissible? Verify your solutions. a.) b.) HO
b.)
Verify 1. It does verify.
x=
a=
Questions from previous page
6.4 Example^1 Continued 3 Check: Substitute z = 5 into the original equation. Left Side Right Side Left Side = Right Side 3
Example 1: Your Turn Answer Solve the equation. What are the nonpermissible values?
Questions from the previous page
- Thus x =
3 6.4 Example^2 Continued (^44) Check: Substitute k = 6 into the original equation. Left Side Right^ Side Left Side = Right Side Therefore, the solution is k = 6. 3 –2 is a nonpermissible value and is called an extraneous solution.
Example 2: Your Turn Answer Solve the equation. What are the nonpermissible values?
15 x 1/ 1/ 1/x x/ x/ 1 8 hours and minutes
70 70 x x 70/x 70/(x6) Both verify and are permissible but only 20 makes sense in the context. 42/176= ve speed