Rút gọn biểu thức: A=1/(x+cănx)−2cănx/(x−1)+1/(x−cănx

* Hướng dẫn giải

$\begin{array}{l}A=\frac{1}{x+\sqrt{x}}-\frac{2\sqrt{x}}{x-1}+\frac{1}{x-\sqrt{x}}\\ =\frac{1}{\sqrt{x}(\sqrt{x}+1)}-\frac{2\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}+\frac{1}{\sqrt{x}(\sqrt{x}-1)}\\ =\frac{(\sqrt{x}-1)-2\sqrt{x}\sqrt{x}+(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+1)}\\ =\frac{-2x+2\sqrt{x}}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+1)}\\ =\frac{-2\sqrt{x}(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+1)}\\ =\frac{-2}{\sqrt{x}+1}\end{array}$