Skip to main content
Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema 29
Capitolo 1, Problema 29

Write each rational expression in lowest terms. See Example 2. (8m² + 6m - 9) / (16m² - 9)

Guida verificata passo dopo passo
1
Start by factoring both the numerator and the denominator of the rational expression separately. The expression is \( \frac{8m^{2} + 6m - 9}{16m^{2} - 9} \).
Factor the numerator \(8m^{2} + 6m - 9\). Look for two numbers that multiply to \(8 \times (-9) = -72\) and add to \(6\). Use these to split the middle term and factor by grouping.
Factor the denominator \(16m^{2} - 9\). Recognize this as a difference of squares, which factors as \(a^{2} - b^{2} = (a - b)(a + b)\).
After factoring numerator and denominator, write the expression as a product of factors over a product of factors.
Cancel out any common factors that appear in both numerator and denominator to write the expression in lowest terms.

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:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Factoring Quadratic Expressions

Factoring involves rewriting a quadratic expression as a product of simpler binomials or polynomials. For example, to simplify rational expressions, you factor both numerator and denominator to identify common factors. Recognizing patterns like the difference of squares or trinomial factoring is essential.
Video consigliato:
Percorso guidato
6:08
Factoring

Difference of Squares

The difference of squares is a special factoring pattern where an expression of the form a² - b² factors into (a - b)(a + b). This is useful for simplifying denominators or numerators that fit this pattern, allowing cancellation of common factors in rational expressions.
Video consigliato:
Percorso guidato
4:47
Sum and Difference of Tangent

Simplifying Rational Expressions

Simplifying rational expressions means reducing them to their lowest terms by factoring numerator and denominator and canceling common factors. This process makes expressions easier to work with and understand, and it is crucial for solving equations or performing further operations.
Video consigliato:
Percorso guidato
2:58
Rationalizing Denominators
Pratica correlata
Domanda del libro di testo

Find each sum or difference. See Example 1. 9⁄10 - ( -4⁄3)

491
views
Domanda del libro di testo

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. See Example 3. Natural numbers

26
views
Domanda del libro di testo

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = ½ x - 2

530
views
Domanda del libro di testo

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

601
views
Domanda del libro di testo

Graph each function. See Examples 1 and 2. h(x) = √4x

680
views
Domanda del libro di testo

Find the square of each radical expression. See Example 2. -√19

804
views