Biểu thức \(P=\left(x^{\frac{1}{2}}-y^{\frac{1}{2}}\right)^2\left(1-2\sqrt{\frac{y}{x}}+\frac{y}{x}\right)^{-1}\) ,\(\left(x,y>0\right)\) rút gọn bằng
\(x\). \(\frac{1}{x^2}\). \(-x\). \(\sqrt{x}\). Hướng dẫn giải:Có \(\left(1-2\sqrt{\dfrac{y}{x}}+\dfrac{y}{x}\right)=\left(1-\sqrt{\dfrac{y}{x}}\right)^2=\left(\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}}\right)^2=\dfrac{\left(x^{\frac{1}{2}}-y^{\frac{1}{2}}\right)^2}{x}\) . Do đó \(P=x\)