y = 2x/√(x2-5x+6)
y2 = 4x2/(x2-5x+6)
Since the numerator and denominator are the same degree, y2 has a horizontal asymptote equal to the ratio of the x2 terms = 4x2/x2 = 4. Since y2 has a vertical asymptote at y=4, y has vertical asymptotes at y = √y2 = √4 = ±2 (x = 2 and x = -2).
BTW, the denominator factors to (x-2)(x-3), so y has vertical asymptotes at x = 2 and x = 3. Click on the link below for the graph.