Domanda del libro di testo
Evaluate each exponential expression: 5-3• 5
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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
Capitolo 1, Problema 26
In Exercises 15–32, multiply or divide as indicated. (x2−4)/(x−2) ÷ (x+2)/(4x−8)
Guida verificata passo dopo passo1
Rewrite the division problem as a multiplication problem by multiplying the first fraction by the reciprocal of the second fraction. This gives: \( \frac{x^2 - 4}{x - 2} \times \frac{4x - 8}{x + 2} \).
Factorize the numerator \(x^2 - 4\) in the first fraction using the difference of squares formula: \(x^2 - 4 = (x - 2)(x + 2)\).
Factorize the numerator \(4x - 8\) in the second fraction by factoring out the greatest common factor (GCF), which is 4: \(4x - 8 = 4(x - 2)\).
Substitute the factored forms into the expression: \( \frac{(x - 2)(x + 2)}{x - 2} \times \frac{4(x - 2)}{x + 2} \).
Simplify the expression by canceling out common factors in the numerator and denominator, such as \(x - 2\) and \(x + 2\), where applicable.
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Rational Expressions
Rational expressions are fractions where the numerator and/or denominator are polynomials. Understanding how to manipulate these expressions, including simplifying, multiplying, and dividing them, is crucial for solving problems involving them. In this question, we are dealing with rational expressions that require simplification before performing operations.
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02:58
Rationalizing Denominators
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of its factors. This is essential for simplifying rational expressions, as it allows us to cancel common factors in the numerator and denominator. In the given expression, recognizing that both the numerator and denominator can be factored will facilitate easier computation.
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07:30Introduction to Factoring Polynomials
Division of Fractions
Dividing fractions involves multiplying by the reciprocal of the divisor. In this case, to divide the first rational expression by the second, we will multiply the first expression by the reciprocal of the second. This concept is fundamental in algebra and is key to solving the problem correctly.
Video consigliato:
05:45Radical Expressions with Fractions
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