\(x-\dfrac{2x-2\sqrt{x}}{\sqrt{x}-1}+\dfrac{x\sqrt{x}+1}{x-\sqrt{x}+1}+1\) (với \(x\ge0,x\ne1\))
\(=x-\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}+\dfrac{\left(\sqrt{x}\right)^3+1^3}{x-\sqrt{x}+1}+1\)
\(=x-\dfrac{2\sqrt{x}}{1}+\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-\sqrt{x}+1\right)}{x-\sqrt{x}+1}+1\)
\(=x-2\sqrt{x}+\left(\sqrt{x}+1\right)+1\)
\(=x-2\sqrt{x}+\sqrt{x}+1+1\)
\(=x-\sqrt{x}+2\)
\(x-\dfrac{2x-2\sqrt{x}}{\sqrt{x}-1}+\dfrac{x\sqrt{x}+1}{x-\sqrt{x}+1}+1\)
=> \(x-\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}+\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{x-\sqrt{x}+1}+1\)
=> \(x-2\sqrt{x}+\sqrt{x}+1+1\)
=> \(x-\sqrt{x}+2\)
