Domanda del libro di testo
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x2−25)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 1
Find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)
Guida verificata passo dopo passo1
Identify the denominator of the rational expression, which is \(x - 3\).
Recall that the domain of a rational expression excludes any values that make the denominator equal to zero, because division by zero is undefined.
Set the denominator equal to zero to find the excluded values: \(x - 3 = 0\).
Solve the equation for \(x\): add 3 to both sides to get \(x = 3\).
Conclude that the number \(x = 3\) must be excluded from the domain of the expression.
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Domain of a Rational Expression
The domain of a rational expression includes all real numbers except those that make the denominator zero. Since division by zero is undefined, these values must be excluded to ensure the expression is valid.
Video consigliato:
02:58
Rationalizing Denominators
Identifying Values That Make the Denominator Zero
To find excluded values, set the denominator equal to zero and solve for the variable. These solutions are the numbers that cannot be in the domain because they cause division by zero.
Video consigliato:
02:58Rationalizing Denominators
Simplifying Rational Expressions
Understanding how to simplify rational expressions helps in identifying restrictions on the domain. Even after simplification, any value that originally made the denominator zero remains excluded from the domain.
Video consigliato:
05:07Simplifying Algebraic Expressions
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