Show all work to identify the asymptotes and zero of the function f(x) = 3x/x^2-9

Answer:[tex] Vertical\: Asymptotes: -3, 3 = x \\ Horizontal\: Asymptote: 0 = y \\ No\: Oblique\: Asymptotes[/tex]Step-by-step explanation:Obviously, −3 and 3 would be set to equal [tex]x[/tex], knowing that they are the roots of 9. Or, you can choose to factor. The divisor of [tex]{x}^{2} - 9[/tex] is a product of two binomials:[tex][x - 3][x + 3][/tex]Then, knowing that you set both factors equal to zero, −3 and 3 would be your zeros, which are also two non-removable discontinuities, or vertical asymptotes because you cannot have zero in the denominator.I am joyous to assist you anytime.