교과서 질문
In Exercises 111–120, use the order of operations to simplify each expression. 102−100÷52⋅2−3
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
1장, 문제 114
Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]
검증된 단계별 안내1
Rewrite the division of fractions as multiplication by the reciprocal. This means the problem becomes: [(x^2 - 5x - 24) / (x^2 - x - 12)] * [(x^2 + x - 6) / (x^2 - 10x + 16)].
Factorize each quadratic expression in the numerators and denominators. For example, factorize x^2 - 5x - 24 into (x - 8)(x + 3), x^2 - x - 12 into (x - 4)(x + 3), x^2 + x - 6 into (x - 2)(x + 3), and x^2 - 10x + 16 into (x - 8)(x - 2).
Substitute the factored forms back into the expression. The problem now looks like: [(x - 8)(x + 3) / (x - 4)(x + 3)] * [(x - 2)(x + 3) / (x - 8)(x - 2)].
Simplify the expression by canceling out common factors in the numerators and denominators. For instance, cancel (x + 3), (x - 8), and (x - 2) where applicable.
After canceling, multiply the remaining terms in the numerators and denominators to get the simplified expression. Ensure no further simplifications are possible.
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4m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial expression as a product of its factors. This is essential for simplifying rational expressions, as it allows for the cancellation of common terms. For example, the polynomial x^2 - 5x - 24 can be factored into (x - 8)(x + 3), making it easier to work with in division or multiplication.
추천 영상:
07:30
Introduction to Factoring Polynomials
Rational Expressions
A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including multiplying and dividing them, is crucial in algebra. When dividing rational expressions, one can multiply by the reciprocal of the divisor, which simplifies the process of finding the result.
추천 영상:
02:58Rationalizing Denominators
Simplifying Complex Fractions
Simplifying complex fractions involves reducing fractions that contain other fractions in their numerators or denominators. This process often requires finding a common denominator and can include factoring and canceling terms. Mastery of this concept is vital for solving problems that involve multiple layers of fractions, as seen in the given question.
추천 영상:
04:22Dividing Complex Numbers
관련 실천
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교과서 질문
In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]
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