find the vertical asymptotes of the graph of the rational functions

Question

This is finding the vertical asymptotes, in any, of the graph of the rational function.

Answer 1

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.