The equations of the vertical asymptotes are the values of the zeroes of the denominator
The given algebraic rational function is

Equate the denominator by 0 to find its roots

Factor the left side

Equate each factor by 0


Then the equations of the vertical asymptotes are

To find the horizontal asymptote
Since the greatest power of up and down is 2
Then divide the coefficients of x^2 up by down
Since the coefficient of x^2 up is 6
Since the coefficient of x^2 down is 2
Since 6/2 = 3
Then the equation of the horizontal asymptote is
