#### Answer

$\text{all real numbers except }$ $
x=\dfrac{17}{6}
$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}
.$