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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 16a
Chapter 1, Problem 16a

Find the domain of each rational expression. 3 / (x2 - 5x - 6)

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Identify the rational expression given: \(\frac{3}{x^2 - 5x - 6}\).
Recall that the domain of a rational expression excludes values that make the denominator equal to zero, because division by zero is undefined.
Set the denominator equal to zero to find the values to exclude: \(x^2 - 5x - 6 = 0\).
Factor the quadratic expression: \(x^2 - 5x - 6 = (x - 6)(x + 1)\).
Solve each factor equal to zero: \(x - 6 = 0\) gives \(x = 6\), and \(x + 1 = 0\) gives \(x = -1\). 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 skill is essential to identify values that make the denominator zero by setting each factor equal to zero and solving for x.
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