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
0. Review of Algebra
Factoring Polynomials
7:41 minutes
Problem 67b
Textbook Question
Textbook QuestionAdd or subtract, as indicated. 4/x + 1 + 1/x^2 - x + 1 - 12/x^3 + 1
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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 adding, subtracting, and simplifying them, is crucial for solving problems involving them. In this question, the expressions contain variables in the denominators, which require careful handling to combine them correctly.
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02:58
Rationalizing Denominators
Common Denominator
To add or subtract rational expressions, it is essential to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators involved. In this case, the denominators are x, x^2, and x^3, and identifying the LCM allows for the expressions to be combined into a single fraction, simplifying the process of addition and subtraction.
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02:58
Rationalizing Denominators
Polynomial Simplification
Polynomial simplification involves combining like terms and reducing expressions to their simplest form. After finding a common denominator and rewriting the rational expressions, it is necessary to combine the numerators and simplify the resulting polynomial. This process ensures that the final answer is presented in the most concise and manageable form.
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Introduction to Polynomials
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