Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Rational Equations
2:56 minutes
Problem 52
Textbook Question
Textbook QuestionExercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2/(x - 2) = x/(x - 2) - 2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Equations
Rational equations are equations that involve fractions with polynomials in the numerator and denominator. To solve these equations, it is essential to identify any restrictions on the variable, particularly values that would make the denominator zero, as these values are not permissible in the solution set.
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Restrictions on Variables
Restrictions on variables in rational equations arise when the denominator equals zero, leading to undefined expressions. Identifying these restrictions is crucial because they determine the valid values for the variable, ensuring that the solutions do not include any values that would invalidate the equation.
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Solving Rational Equations
To solve rational equations, one typically eliminates the denominators by multiplying both sides of the equation by the least common denominator (LCD). After simplifying, the resulting equation can be solved for the variable, while always considering the previously identified restrictions to ensure the solutions are valid.
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