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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 15a
Chapter 1, Problem 15a

Find the domain of each rational expression. 12/ (x2 + 5x + 6)

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Identify the rational expression given: \(\frac{12}{x^2 + 5x + 6}\).
Recall that the domain of a rational expression excludes values of \(x\) that make the denominator equal to zero, because division by zero is undefined.
Set the denominator equal to zero to find these excluded values: \(x^2 + 5x + 6 = 0\).
Factor the quadratic expression in the denominator: \(x^2 + 5x + 6 = (x + 2)(x + 3)\).
Solve each factor set to zero: \(x + 2 = 0\) gives \(x = -2\), and \(x + 3 = 0\) gives \(x = -3\). These values are excluded from the domain.

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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, evaluate, and find restrictions on the variable to avoid division by zero.
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Domain of a Function

The domain of a function is the set of all possible 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 Quadratic Expressions

Factoring quadratics involves rewriting a quadratic polynomial as a product of two binomials. This helps identify values that make the denominator zero by setting each factor equal to zero, which is essential for determining the domain restrictions.
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