Question 625809
Describe the vertical asymptote(s) and hole(s) for the graph of 
{{{y = (x - 3)(x - 1)/(x - 1)(x - 5)}}}
(x-1) cancels out, leaving the graph of {{{ (x-3)/(x-5)}}} 
The asymptote for this graph is x=5, at which point the curve is undefined.
Also a hole occurs at x=1 which means x=1 is not in the domain of y.
So you have an asymptote at x=5 and a hole at x=1
see graph below as a visual check:

{{{ graph( 300, 300, -10, 10, -10, 10, (x-3)/(x-5)) }}}