Chapter 7 - Rational Functions - 7.1 Rational Functions and Variation - 7.1 Exercises: 29

$\text{all real numbers except }$ $x= 3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given rational function, $f(x)=\dfrac{x+5}{x-3} ,$ are the values of $x$ which will NOT make the denominator equal to $0.$ $\bf{\text{Solution Details:}}$ Solving for the values of $x$ that will make the denominator equal to $0$ results to \begin{array}{l}\require{cancel} x-3=0 \\\\ x=3 .\end{array} Hence, the domain is the set of $\text{all real numbers except }$ $x= 3 .$

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