Skip to main content
Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 30
Capitolo 1, Problema 30

In Exercises 15–32, multiply or divide as indicated. (x2−4)/(x2+3x−10) ÷ (x2+5x+6)/(x2+8x+15)

Guida verificata passo dopo passo
1
Rewrite the division of fractions as multiplication by the reciprocal. This means flipping the second fraction. The expression becomes: ((x^2−4)/(x^2+3x−10)) * ((x^2+8x+15)/(x^2+5x+6)).
Factorize all the polynomials in the numerators and denominators. For example: x^2−4 is a difference of squares and factors as (x−2)(x+2). Similarly, factorize x^2+3x−10, x^2+8x+15, and x^2+5x+6.
After factoring, the expression will look like: (((x−2)(x+2))/((x+5)(x−2))) * (((x+3)(x+5))/((x+3)(x+2))).
Cancel out any common factors in the numerators and denominators across the multiplication. For instance, (x−2), (x+2), (x+5), and (x+3) may cancel out depending on their positions.
Write the simplified expression after canceling the common factors. This will be the final simplified result of the given problem.

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:
3m

Concetti chiave

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

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including simplifying, multiplying, and dividing them, is crucial for solving problems involving them. For example, recognizing that (x^2−4) can be factored into (x−2)(x+2) helps in simplifying the expression.
Video consigliato:
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 for cancellation of common factors. For instance, the polynomial x^2 + 3x - 10 can be factored into (x + 5)(x - 2), which simplifies the division process.
Video consigliato:
07:30
Introduction to Factoring Polynomials

Division of Rational Expressions

Dividing rational expressions involves multiplying by the reciprocal of the divisor. This means that to divide (x^2−4)/(x^2+3x−10) by (x^2+5x+6)/(x^2+8x+15), you first factor both expressions and then multiply by the reciprocal of the second expression. This process is fundamental in solving complex rational equations.
Video consigliato:
02:58
Rationalizing Denominators
Pratica correlata
Domanda del libro di testo

In Exercises 15–58, find each product. (7x3+5)(x2−2)

736
views
Domanda del libro di testo

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x

1416
views
Domanda del libro di testo

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 9x2+5x−4

186
views
Domanda del libro di testo

Simplify each exponential expression in Exercises 23–64. (x11)5(x^{11})^5

902
views
Domanda del libro di testo

Find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}

909
views
Domanda del libro di testo

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. 150x43x\(\frac{\sqrt{150x^4}\)}{\(\sqrt{3x}\)}

642
views