Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.
consider the following equation:
This is a rational function. More to the point, this is a fraction. You can't have a 0 in the denominator of a fraction. So if I set the denominator of the above fraction equal to zero and solve, this will tell me the values that xcannot be:
x2 – 5x – 6 = 0
(x – 6)(x + 1) = 0
x = 6 or –1
So x cannot be 6 or –1, because then I'd be dividing by zero.