## Intermediate Algebra: Connecting Concepts through Application

$\text{all real numbers except }$ $x=\dfrac{17}{6}$
$\bf{\text{Solution Outline:}}$ The domain of the given rational function, $f(x)=\dfrac{2x-7}{6x-17} ,$ 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} 6x-17=0 \\\\ 6x=17 \\\\ x=\dfrac{17}{6} .\end{array} Hence, the domain is the set of $\text{all real numbers except }$ $x=\dfrac{17}{6} .$