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
The Square Root Property
3:45 minutes
Problem 108
Textbook Question
Textbook QuestionSolve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including finding a common denominator and simplifying, is crucial for solving equations involving them. In this problem, the presence of rational expressions requires careful handling to avoid undefined values.
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02:58
Rationalizing Denominators
Finding Common Denominators
To solve equations involving rational expressions, it is often necessary to find a common denominator. This allows for the combination of fractions into a single expression, making it easier to isolate variables. In this case, identifying the least common denominator will help simplify the equation and facilitate solving for x.
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Rationalizing Denominators
Factoring Polynomials
Factoring polynomials is the process of breaking down a polynomial into simpler components, or factors, that can be multiplied together to yield the original polynomial. This concept is essential in this problem, particularly for simplifying the right side of the equation and solving for x, as it can reveal potential solutions and help identify restrictions on the variable.
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