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
Polynomials Intro
3:40 minutes
Problem 24
Textbook Question
Textbook QuestionIn Exercises 15–32, multiply or divide as indicated. (x+5)/7 ÷ (4x+20)/9
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Fraction Division
Dividing fractions involves multiplying by the reciprocal of the divisor. In this case, to divide (x+5)/7 by (4x+20)/9, you first rewrite the division as multiplication by the reciprocal: (x+5)/7 * (9/(4x+20)). This process simplifies the operation and allows for easier manipulation of the fractions.
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Factoring Polynomials
Factoring is the process of breaking down a polynomial into simpler components, or factors, that can be multiplied together to yield the original polynomial. In the expression (4x+20), you can factor out the common term, resulting in 4(x+5). This simplification is crucial for reducing fractions and making calculations more manageable.
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Simplifying Rational Expressions
Simplifying rational expressions involves reducing fractions to their simplest form by canceling out common factors in the numerator and denominator. After rewriting the division as multiplication and factoring, you can cancel out the (x+5) terms, leading to a more straightforward expression that is easier to evaluate or further manipulate.
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