Domanda del libro di testo
In Exercises 57–64, factor using the formula for the sum or difference of two cubes. 8x^3+125
1019
views
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 64
In Exercises 33–68, add or subtract as indicated. x/(x2−2x−24) − x/(x2−7x+6)
Guida verificata passo dopo passo1
Factorize the denominators of both fractions. For the first denominator, \(x^2 - 2x - 24\), find two numbers that multiply to \(-24\) and add to \(-2\). For the second denominator, \(x^2 - 7x + 6\), find two numbers that multiply to \(6\) and add to \(-7\).
Rewrite the fractions with the factored denominators. The first fraction becomes \(\frac{x}{(x - 6)(x + 4)}\), and the second fraction becomes \(\frac{x}{(x - 6)(x - 1)}\).
Identify the least common denominator (LCD) of the two fractions. The LCD is the product of all unique factors in the denominators: \((x - 6)(x + 4)(x - 1)\).
Rewrite each fraction with the LCD as the denominator. Multiply the numerator and denominator of the first fraction by \((x - 1)\), and the numerator and denominator of the second fraction by \((x + 4)\). This gives \(\frac{x(x - 1)}{(x - 6)(x + 4)(x - 1)}\) and \(\frac{x(x + 4)}{(x - 6)(x + 4)(x - 1)}\).
Combine the fractions by subtracting the numerators over the common denominator. Simplify the numerator \(x(x - 1) - x(x + 4)\) and leave the denominator as \((x - 6)(x + 4)(x - 1)\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial expression as a product of its factors. This is essential for simplifying expressions and finding common denominators in rational expressions. For example, the quadratic expressions in the denominators, x^2 - 2x - 24 and x^2 - 7x + 6, can be factored to facilitate addition or subtraction.
Video consigliato:
07:30
Introduction to Factoring Polynomials
Common Denominator
A common denominator is a shared multiple of the denominators of two or more fractions. When adding or subtracting rational expressions, it is necessary to express each fraction with the same denominator to combine them effectively. In this case, finding the least common denominator (LCD) of the two factored expressions is crucial for performing the operation.
Video consigliato:
02:58Rationalizing Denominators
Rational Expressions
Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including addition, subtraction, multiplication, and division, is fundamental in algebra. In this problem, the operation involves subtracting two rational expressions, which requires careful handling of the numerators and the common denominator.
Video consigliato:
02:58Rationalizing Denominators
Pratica correlata
Domanda del libro di testo
In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x4 y2+5x3 y−3y)−(2x4 y2−3x3 y−4y+6x)
1021
views
Domanda del libro di testo
Simplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0
961
views
Domanda del libro di testo
Evaluate each expression 161/2.
1313
views
Domanda del libro di testo
Evaluate each expression 1251/3.
1308
views
Domanda del libro di testo
Write each number in decimal notation without the use of exponents.
1037
views