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vertical asymptote is x=3/5, so cx+d = 5x-3
horizontal asymptote is y=4/3, so a/c = 4/3, making a = 20/3
Now we have
y = (20/3 x + b)/(5x-3) and y(0) = 2, so
b/-3 = 2, making b = -6
y = (20/3 x - 6)/(5x-3) = (20x-18)/(15x-9)