Question
Fill each blank so that the resulting statement is true.
The set of real numbers for which a rational expression is defined is the ___ of the expression. One must exclude all numbers from this set that make the
denominator of the rational expression
The set of real numbers for which a rational expression is defined is the ___ of the expression. One must exclude all numbers from this set that make the
denominator of the rational expression
Ask by Davison Pearson. in the United States
Mar 29,2025
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Answer
The set of real numbers for which a rational expression is defined is the domain of the expression. One must exclude all numbers from this set that make the denominator of the rational expression equal to zero.
Solution
To fill in the first blank, we need to identify the term that describes the set of real numbers for which a rational expression is defined. This term is known as the “domain” of the expression.
For the second blank, we need to specify what must be excluded from the domain. We must exclude all numbers that make the denominator of the rational expression equal to zero, as these values would make the expression undefined.
For the second blank, we need to specify what must be excluded from the domain. We must exclude all numbers that make the denominator of the rational expression equal to zero, as these values would make the expression undefined.
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Simplify this solution Beyond the Answer
The set of real numbers for which a rational expression is defined is the domain of the expression. One must exclude all numbers from this set that make the denominator of the rational expression equal to zero to ensure the expression remains valid and avoids undefined values.
Understanding this concept is crucial for working with rational expressions, as it sets the foundation for algebraic manipulations, helps in graphing functions, and is essential in calculus when dealing with limits and continuity.
