1Cademy - Example of Determining the Domain of the Rational Function $$R(x) = \frac{2x^2 - 10x}{4x^2 - 16x

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Procedure for Determining the Domain of a Rational Function

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Example of Determining the Domain of the Rational Function $R(x) = \frac{2x^2 - 10x}{4x^2 - 16x - 20}$

To find the domain of the rational function $R(x) = \frac{2x^2 - 10x}{4x^2 - 16x - 20}$ , we follow the procedure to determine the domain of a rational function by finding and excluding values that cause division by zero.

Step 1. Set the denominator equal to zero: $4x^2 - 16x - 20 = 0$ .

Step 2. Solve the equation. First, factor out the greatest common factor: $4(x^2 - 4x - 5) = 0$ . Next, factor the trinomial: $4(x - 5)(x + 1) = 0$ . Using the Zero Product Property, set each variable factor to zero: $x - 5 = 0$ or $x + 1 = 0$ . Solving these equations yields $x = 5$ and $x = -1$ .

Step 3. The domain is all real numbers excluding those values found in Step 2. Therefore, the domain of $R(x)$ is all real numbers where $x eq 5$ and $x eq -1$ .

Updated 2026-05-26

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OpenStax Intermediate Algebra

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