Question

Rút gọn biểu thức \(p=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right).\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)

GIÚP MÌNH VỚI

Answer 1

ĐKXĐ:...

\(P=\left(\frac{\sqrt{x}+\sqrt{x-1}}{x-\left(x-1\right)}-\frac{\left(x-3\right)\left(\sqrt{x-1}+\sqrt{2}\right)}{x-1-2}\right).\left(\frac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}\right)\)

\(=\left(\sqrt{x}+\sqrt{x-1}-\sqrt{x-1}-\sqrt{2}\right).\left(\frac{\sqrt{x}-\sqrt{2}}{-\sqrt{x}\left(\sqrt{x}-\sqrt{2}\right)}\right)\)

\(=\frac{\sqrt{x}-\sqrt{2}}{-\sqrt{x}}=\frac{\sqrt{2}-\sqrt{x}}{\sqrt{x}}\)