\(P=\dfrac{1}{x}\left(\dfrac{\sqrt{x+1}+\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}}+\dfrac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}\right)=\dfrac{1}{x}\left[\dfrac{\left(\sqrt{x+1}+\sqrt{x-1}\right)^2+\left(\sqrt{x+1}-\sqrt{x-1}\right)^2}{\sqrt{\left(x+1\right)}^2-\sqrt{\left(x-1\right)^2}}\right]=\dfrac{1}{x}\left(\dfrac{x+1+2\sqrt{\left(x-1\right)\left(x+1\right)}+x-1+x+1-2\sqrt{\left(x-1\right)\left(x+1\right)}+x-1}{x+1-x+1}\right)=\dfrac{1}{x}\cdot\dfrac{4x}{2}=\dfrac{1}{x}\cdot2x=2\)
=> Giá trị của biểu thức P không phụ thuộc vào biến