Question

rút gọn biểu thức

P=\(\dfrac{8-x}{2-\sqrt[3]{x^2}}:\left(2+\dfrac{\sqrt[3]{x^2}}{2+\sqrt[3]{x}}\right)+\left(\sqrt[3]{x}+\dfrac{2\sqrt[3]{x}}{\sqrt[3]{x}-2}\right)\left(\dfrac{\sqrt[3]{x^2}-4}{\sqrt[3]{x^2}+2\sqrt[3]{x}}\right)\)

Answer 1

\(=\dfrac{\left(2-\sqrt[3]{x}\right)\left(4+2\sqrt[3]{x}+\sqrt[3]{x^2}\right)}{2-\sqrt[3]{x^2}}:\dfrac{4+2\sqrt[3]{x}+\sqrt[3]{x^2}}{2+\sqrt[3]{x}}+\dfrac{\sqrt[3]{x^2}}{\sqrt[3]{x}-2}\cdot\dfrac{\sqrt[3]{x^2}-4}{\sqrt[3]{x^2}+2\sqrt[3]{x}}\)

\(=\dfrac{\left(2-\sqrt[3]{x}\right)\left(2+\sqrt[3]{x}\right)}{2-\sqrt[3]{x^2}}+\dfrac{\sqrt[3]{x^2}\cdot\left(\sqrt[3]{x}+2\right)}{\sqrt[3]{x}\left(\sqrt[3]{x}+2\right)}\)

\(=1+\sqrt[3]{x}\)