Whats the solution for this problem?

First we factor the two equations to get:

(x - 6)(x - 1) / (x - 6)(x + 6).

The (x - 6) represents a hole in the graph so those cancel out. 

To find the vertical asymptote, take the remaining binomial(s) and set them equal to zero. 

x + 6 = 0
x = - 6

There is a vertical asymptote at x = - 6. 

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