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Because of the denominator x^(1/5), the function you are considering is not defined at $x=0$.

Because of the denominator x^(1/5), the function you are considering is not defined at $x=0$.$x=0$. You can have a look at its plot to get convinced:

sage: f = 4/5*(x - 1)^2/x^(1/5) + 2*(x - 1)*x^(4/5)
sage: f.plot(0,1)