Domanda del libro di testo
In Exercises 107–110, use graphs to find each set. (-2,1] ∩ [-1,3)
521
views
Ch. 1 - Equations and Inequalities
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 2, Problema 106
Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4
Guida verificata passo dopo passo1
Identify the equation: \(\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{4}\).
Find the least common denominator (LCD) for the fractions, which is \(4x(x + 3)\).
Multiply both sides of the equation by the LCD to eliminate the denominators: \(4x(x + 3) \times \left( \frac{1}{x} + \frac{1}{x + 3} \right) = 4x(x + 3) \times \frac{1}{4}\).
Simplify each term after multiplication: \(4(x + 3) + 4x = x(x + 3)\).
Rewrite the equation and expand all terms to form a quadratic equation: \(4x + 12 + 4x = x^2 + 3x\), then combine like terms and set the equation to zero.
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:
4mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Solving Rational Equations
Rational equations involve expressions with variables in the denominator. To solve them, find a common denominator to combine terms or clear denominators by multiplying both sides, ensuring to check for excluded values that make denominators zero.
Video consigliato:
05:56
Introduction to Rational Equations
Finding the Least Common Denominator (LCD)
The LCD is the smallest expression that all denominators divide into evenly. Identifying the LCD allows you to combine fractions or eliminate denominators by multiplying through, simplifying the equation to a polynomial or linear form.
Video consigliato:
03:42Rationalizing Denominators Using Conjugates
Checking for Extraneous Solutions
When solving rational equations, some solutions may make denominators zero, which are invalid. After finding potential solutions, substitute them back into the original equation to ensure they do not cause division by zero.
Video consigliato:
05:21Restrictions on Rational Equations
Pratica correlata
Domanda del libro di testo
Solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]
850
views
Domanda del libro di testo
When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.
1211
views
Domanda del libro di testo
Use the table to solve each inequality. - 3 < 2x - 5 ≤ 3
773
views
Domanda del libro di testo
Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)
667
views
Domanda del libro di testo
Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3
844
views