Cho biểu thức: P=căn x/(căn x+2)+(−x+xcănx+6)/(x+cănx−2)−(cănx+1)/(cănx−1) với

* Hướng dẫn giải

Ta có:

$$\begin{gathered} P=\frac{\sqrt{x}}{\sqrt{x}+2}+\frac{-x+x\sqrt{x}+6}{x+\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}-1} \\ =\frac{\sqrt{x}\left(\sqrt{x}-1\right)-x+x\sqrt{x}+6-\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)} \\ =\frac{x-\sqrt{x}-x+x\sqrt{x}+6-x-3\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)} \\ =\frac{-x+x\sqrt{x}-4\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\frac{\left(\sqrt{x}-1\right)\left(x-4\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)} \\ =\sqrt{x}-2 \end{gathered}$$