Question

Describe the vertical asymptote (s) and hole(s) for the graph of y= (x-3)(x-1)/(x-1)(x-5)

Answer 1

In the denominator of the fraction is given expression
`(x-1)(x-5).` This means that

`x\\eq 1,\\x\\eq 5.`

Now simplify the expression
`y=((x-3)(x-1))/((x-1)(x-5)):`

`y=((x-3)(x-1))/((x-1)(x-5))=(x-3)/(x-5).`

This means that
`x=5` is the equation of vertical asymptote and, therefore, since function id not defined for
`x=1` this point is hole of the function.