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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 19a
Chapter 1, Problem 19a

Find the domain of each rational expression. x3 - 1 / x - 1

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Identify the rational expression given: \(\frac{x^3 - 1}{x - 1}\).
Recall that the domain of a rational expression excludes values that make the denominator zero, because division by zero is undefined.
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 \((-\infty, 1) \cup (1, \infty)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials. Understanding rational expressions involves knowing how to simplify, factor, and analyze these fractions, especially focusing on restrictions caused by the denominator.
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Domain of a Function

The domain of a function is the set of all input values (x-values) for which the function is defined. For rational expressions, the domain excludes values that make the denominator zero, as division by zero is undefined.
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Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials. This skill helps identify values that make the denominator zero by factoring and setting each factor equal to zero to find restrictions on the domain.
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