Question

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Answer 1

$(\dfrac{1+x}{\sqrt[3]{x}+1}-\sqrt[3]{x^2})(x^{-\frac{1}{3}}\cdot\sqrt[3]{x}):(1-\dfrac{1}{\sqrt[3]{x}+1})=\\\\=(\dfrac{(\sqrt[3]{x}+1)(\sqrt[3]{x^2}-\sqrt[3]{x}+1)}{\sqrt[3]{x}+1}-\sqrt[3]{x^2})(x^{-\frac{1}{3}}\cdot x^{\frac{1}{3}}):\dfrac{\sqrt[3]{x}+1-1}{\sqrt[3]{x}+1}=\\\\ =(1-\sqrt[3]{x})\cdot \dfrac{1+\sqrt[3]{x}}{\sqrt[3]{x}}=\dfrac{1-\sqrt[3]{x^2}}{\sqrt[3]{x}}.$