Ta có
$\underset{x \to 1}{\lim} \dfrac{\sqrt{2x-1} - 1 + x^2 - 3x + 2}{\sqrt[3]{x-2} + 1 + x^2-x} = \underset{x \to 1}{\lim} \dfrac{\frac{2x-2}{\sqrt{2x-1} + 1} + (x-1)(x-2)}{\frac{x-2+1}{\sqrt[3]{(x-2)^2} - \sqrt[3]{x-2} + 1} + x(x-1)}$
$= \underset{x \to 1}{\lim} \dfrac{\frac{2}{\sqrt{2x-1} + 1} + (x-2)}{\frac{1}{\sqrt[3]{(x-2)^2} - \sqrt[3]{x-2} + 1} + x}$
$= \dfrac{\frac{2}{\sqrt{2-1} + 1} + 1-2}{\frac{1}{\sqrt[3]{(1-2)^2} - \sqrt[3]{1-2} +1} + 1}$
$= 0$
