Domanda del libro di testo
Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)
189
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 115
Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]
Guida verificata passo dopo passo1
Step 1: Recognize that the denominators in both fractions are the same, \(x^2 - 9\). This means we can combine the numerators directly by subtraction.
Step 2: Write the combined fraction as \(\frac{(2x - 7) - (x - 10)}{x^2 - 9}\). Be careful to distribute the negative sign across the second numerator.
Step 3: Simplify the numerator by combining like terms. Expand \((2x - 7) - (x - 10)\) to \(2x - 7 - x + 10\), which simplifies to \(x + 3\).
Step 4: Rewrite the fraction as \(\frac{x + 3}{x^2 - 9}\).
Step 5: Factor the denominator \(x^2 - 9\) using the difference of squares formula: \(x^2 - 9 = (x - 3)(x + 3)\). Check if the numerator \(x + 3\) can cancel with a factor in the denominator.
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.
Common Denominator
In order to add or subtract fractions, they must have a common denominator. In this case, both fractions share the denominator (x^2 - 9), which simplifies the process. When the denominators are the same, you can combine the numerators directly while keeping the common denominator intact.
Video consigliato:
02:58
Rationalizing Denominators
Factoring Polynomials
Factoring is the process of breaking down a polynomial into simpler components, or factors, that can be multiplied together to obtain the original polynomial. In this problem, recognizing that x^2 - 9 can be factored into (x - 3)(x + 3) is crucial for simplifying the expression and understanding its behavior.
Video consigliato:
07:30Introduction to Factoring Polynomials
Simplifying Rational Expressions
Simplifying rational expressions involves reducing the expression to its simplest form by canceling out common factors in the numerator and denominator. After combining the fractions, it is important to simplify the resulting expression to make it easier to interpret and work with, ensuring that any restrictions on the variable are also noted.
Video consigliato:
05:07Simplifying Algebraic Expressions
Pratica correlata
Domanda del libro di testo
In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)
158
views
Domanda del libro di testo
Add or subtract as indicated. 12/25x^2+11/15x^3
139
views
Domanda del libro di testo
In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2
897
views
Domanda del libro di testo
In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]
240
views
Domanda del libro di testo
Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]
163
views