Textbook Question
Write each improper fraction as a mixed number. 17/12
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Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 1, Problem 17a
Find the domain of each rational expression. x2 - 1 / x + 1
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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 zero.
Set the denominator equal to zero to find the values to exclude: \(x + 1 = 0\).
Solve for \(x\): \(x = -1\).
Conclude that the domain is all real numbers except \(x = -1\).
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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, manipulate, and analyze these fractions, especially focusing on restrictions caused by the denominator.
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Rationalizing Denominators
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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3:51Domain Restrictions of Composed Functions
Finding Restrictions by Setting the Denominator Equal to Zero
To find the domain of a rational expression, set the denominator equal to zero and solve for x. The solutions are excluded from the domain because they cause division by zero, which is undefined in mathematics.
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03:42Finding Zeros & Their Multiplicity
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