Asymptote bei b=2, wenn α=β

b = 2 (slider from -5 to 5, step 0.2)
α = 2 (slider from 0 to 5, step 1)
β = 2 (slider from 0 to 5, step 1)
g(x) = (x * (x - 2)^(β))
h(x) = (((x - 1) * (x - b)^(α)) * (x - 3))
f(x) = h(x) / g(x)
p(x) = 1 / g(x)
gl1: x = 2
B: (b, 0)
Text1: "f(x)=" + (LaTeX[f]) + ""
A = (-1.9530169100414636, 0.8553567694249133)
C = (-1.0008972056967715, 0.8553567694249133)
f_p = PartialFractions(f)
Text2: "f_p(x)=" + f_p + ""
q: y = x - 4
a = false