교과서 질문
Evaluate each exponential expression in Exercises 1–22.
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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 16
Multiply or divide as indicated.
검증된 단계별 안내1
Start by writing the expression clearly: \(\frac{6x+9}{3x-15} \cdot \frac{x-5}{4x+6}\).
Factor all polynomials in the numerators and denominators where possible. For example, factor out the greatest common factor (GCF) from each: \(6x+9 = 3(2x+3)\), \(3x-15 = 3(x-5)\), and \(4x+6 = 2(2x+3)\).
Rewrite the expression using the factored forms: \(\frac{3(2x+3)}{3(x-5)} \cdot \frac{x-5}{2(2x+3)}\).
Look for common factors in the numerators and denominators across the entire expression that can be canceled out. Cancel these common factors to simplify the expression.
After canceling, multiply the remaining numerators together and the remaining denominators together to write the simplified product as a single fraction.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Factoring Polynomials
Factoring involves rewriting polynomials as products of simpler expressions. This is essential for simplifying rational expressions by canceling common factors. For example, 6x + 9 can be factored as 3(2x + 3), and 3x - 15 as 3(x - 5).
추천 영상:
07:30
Introduction to Factoring Polynomials
Multiplication of Rational Expressions
Multiplying rational expressions involves multiplying the numerators together and the denominators together. After multiplication, the expression should be simplified by factoring and canceling common factors to reduce it to simplest form.
추천 영상:
02:58Rationalizing Denominators
Simplifying Rational Expressions
Simplifying rational expressions means reducing them to their simplest form by canceling common factors in the numerator and denominator. This requires identifying and factoring expressions fully to see which terms can be canceled.
추천 영상:
05:07Simplifying Algebraic Expressions
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교과서 질문
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). (2x+3y)/(x+1), for x=-2 and y=4
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교과서 질문
Evaluate each exponential expression in Exercises 1–22.
1161
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