Question

Rút gọn biểu thức:

\(P=\left(\frac{2\sqrt[3]{2}\cdot xy}{x^2y^2-\sqrt[3]{4}}+\frac{xy-\sqrt[3]{2}}{2xy+2\sqrt[3]{2}}\right)\cdot\frac{2xy}{xy+\sqrt[3]{2}}-\frac{xy}{xy-\sqrt[3]{2}}\)

Answer 1

Đặt \(\sqrt[3]{2}=z\)

\(P=\left(\frac{2xyz}{x^2y^2-z^2}+\frac{xy-z}{2\left(xy+z\right)}\right).\frac{2xy}{xy+z}-\frac{xy}{xy-z}\)

\(=\left(\frac{4xyz}{2\left(xy-z\right)\left(xy+z\right)}+\frac{\left(xy-z\right)^2}{2\left(xy-z\right)\left(xy+z\right)}\right).\frac{2xy}{xy+z}-\frac{xy}{xy-z}\)

\(=\frac{\left(xy+z\right)^2}{2\left(xy-z\right)\left(xy+z\right)}.\frac{2xy}{\left(xy+z\right)}-\frac{xy}{xy-z}\)

\(=\frac{xy}{xy-z}-\frac{xy}{xy-z}=0\)