1,\(K=\dfrac{x}{\sqrt{x}-1}-\dfrac{2x-\sqrt{x}}{x-\sqrt{x}}\)
\(\Rightarrow K=\dfrac{x\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{2x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(\Rightarrow K=\dfrac{x\sqrt{x}-2x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(\Rightarrow K=\dfrac{\sqrt{x}\left(x-2\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(\Rightarrow K=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(\Rightarrow K=\sqrt{x}-1\)
b, Thay \(x=4+2\sqrt{3}.vào.K\Rightarrow K=\sqrt{4+2\sqrt{3}}-1=\sqrt{3+2\sqrt{3}.1+1}-1=\sqrt{\left(\sqrt{3}+1\right)^2}-1=\sqrt{3}+1-1=\sqrt{3}\)
