Find the domain of each rational expression. See Example 1. (x² - 1) / (x + 1)

Guida verificata passo dopo passo

Identify the rational expression given: \(\frac{x^{2} - 1}{x + 1}\).

Recall that the domain of a rational expression includes all real numbers except those that make the denominator equal to zero.

Set the denominator equal to zero and solve for \(x\): \(x + 1 = 0\).

Solve the equation to find the value(s) to exclude from the domain: \(x = -1\).

Conclude that the domain is all real numbers except \(x = -1\), which can be written in interval notation as \((-\infty, -1) \cup (-1, \infty)\).

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:

Concetti chiave

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

Domain of a Rational Expression

The domain of a rational expression includes all real numbers except those that make the denominator zero, as division by zero is undefined. To find the domain, identify values that cause the denominator to be zero and exclude them.

Video consigliato:

Percorso guidato

2:58

Rationalizing Denominators

Factoring Polynomials

Factoring polynomials involves rewriting expressions as products of simpler polynomials. For example, x² - 1 factors into (x - 1)(x + 1). Factoring helps simplify expressions and identify zeros of numerator and denominator.

Video consigliato:

Percorso guidato

6:08

Factoring

Simplifying Rational Expressions

Simplifying rational expressions means reducing them by canceling common factors in numerator and denominator. However, restrictions on the domain remain based on the original denominator, even if factors cancel out.

Video consigliato:

Percorso guidato

2:58

Rationalizing Denominators

Pratica correlata

Domanda del libro di testo

Determine whether each relation defines a function. See Example 1. x y 3 -4 7 -4 10 -4

636

views

Domanda del libro di testo

Find each square root. See Example 1. -√256

1021