The function given is,
[tex]y=\frac{x-6}{(x-1)(x-6)}[/tex]
Since , the leading coefficient of numerator is less than the leading coefficient of denominator .
Therefore, there is no horizontal asymptotes.
For finding the vertical asymptotes, substitute the denominator is equal to 0.
[tex](x-1)=0\text{ , }(x-6)=0[/tex][tex]x=\text{ 1,6.}[/tex]
The vertical asymptotes are 1 and 6.
To find the hole in the function,
[tex](x-6)[/tex]
is crossed out in numerator and denominator.
So, if we set up x-6 equals to 0.
The hole in the function is, when
[tex]x=6.[/tex]
