find the vertical asymptotes of the function

Question

f(x)=(x^2-36)/x^2-8x+15)

Answer 1

The funciton is f(x) = (x^2 - 36) / (x^2 - 8x + 15)

To find out vertical asymptote equate denominator to zero and solve for 'x'

x^2 - 8x + 15  =  0

x^2 - 5x - 3x + 15  =  0

x(x - 5) - 3(x - 5)  =  0

(x - 3)(x - 5)  =  0

(x - 3)  =  0       ;        (x - 5)  =  0

x  =  3       ;        x  =  5

Answer :

The vertical asymptotes are the lines x  =  3  and  x  =  5.