#### Answer

The given statement does not make sense. The graph has a vertical asymptote only at $x=2$

#### Work Step by Step

The given function is $f\left( x \right)=\frac{x-1}{\left( x-1 \right)\left( x-2 \right)}$.
Simplifying the above function as,
$\begin{align}
& f\left( x \right)=\frac{x-1}{\left( x-1 \right)\left( x-2 \right)} \\
& =\frac{1}{\left( x-2 \right)}
\end{align}$
Now, the vertical asymptotes is determined by equating the denominator to 0; thus, we’ll get
$\begin{align}
& x-2=0 \\
& x=2
\end{align}$
Therefore, the vertical asymptote is $x=2$ and there is no vertical asymptote at $x=1$. Thus, the given statement does not make sense.