Question

Need help.... Solve this question step by step please.... thank you

Answer 1

$\lim\limits_{x\to 1} \left(\dfrac{2}{\sqrt[3]{x}-1} - \dfrac{\sqrt[3]{x^2}+\sqrt[3]{x}+4}{x-1}\right)\\=\lim\limits_{x\to 1}\left(\dfrac{2}{\sqrt[3]{x}-1} - \dfrac{\sqrt[3]{x^2}+\sqrt[3]{x}+4}{(\sqrt[3]{x})^3 - 1^3}\right)\\=\lim\limits_{x\to 1}\left(\dfrac{2}{\sqrt[3]{x}-1} - \dfrac{\sqrt[3]{x^2}+\sqrt[3]{x}+4}{(\sqrt[3]{x} - 1)(\sqrt[3]{x^2}+\sqrt[3]{x}+1)}\right)\\=\lim\limits_{x\to 1}\dfrac{\sqrt[3]{x^2}+\sqrt[3]{x}-2}{(\sqrt[3]{x} - 1)(\sqrt[3]{x^2}+\sqrt[3]{x}+1)}\\=\lim\limits_{x\to 1}\dfrac{(\sqrt[3]{x} - 1)(\sqrt[3]{x}+2)}{(\sqrt[3]{x} - 1)(\sqrt[3]{x^2}+\sqrt[3]{x}+1)}\\=\lim\limits_{x\to 1}\frac{\sqrt[3]{x}+2}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}\\=1$