Biểu thức \(M=\left(x^{\frac{1}{2}}-y^{\frac{1}{2}}\right)^2\left(1-2\sqrt{\dfrac{y}{x}}+\dfrac{y}{x}\right)^{-1}\) rút gọn bằng
\(x\). \(\frac{1}{x}\). \(-x\). \(\sqrt{x}\). Hướng dẫn giải:\(M=\left(x^{\frac{1}{2}}-y^{\frac{1}{2}}\right)^2\left(1-2\sqrt{\dfrac{y}{x}}+\dfrac{y}{x}\right)^{-1}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2\left[\left(1-\sqrt{\dfrac{y}{x}}\right)^2\right]^{-1}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2\left(\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}}\right)^{-2}\)
\(=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^{2-2}}{\left(\sqrt{x}\right)^{-2}}=\left(\sqrt{x}-\sqrt{y}\right)^0.x=x\)