a) \(A=\dfrac{x\sqrt{2x}+1}{x-1}-\dfrac{x+\sqrt{2x}}{x-1}\left(đk:x\ge0,x\ne1\right)\)
\(=\dfrac{x\sqrt{2x}+1-x-\sqrt{2x}}{x-1}=\dfrac{\sqrt{2x}\left(x-1\right)-\left(x-1\right)}{x-1}=\dfrac{\left(x-1\right)\left(\sqrt{2x}-1\right)}{x-1}=\sqrt{2x}-1\)
\(B=\sqrt{2}.\sqrt{2+\sqrt{3}}-\dfrac{2}{\sqrt{3}+1}=\sqrt{4+2\sqrt{3}}-\dfrac{2\left(\sqrt{3}-1\right)}{2}=\sqrt{\left(\sqrt{3}+1\right)^2}-\dfrac{2\left(\sqrt{3}-1\right)}{2}=\sqrt{3}+1-\sqrt{3}+1=2\)
b) \(A=\sqrt{2x}-1=\sqrt{2B}-1=\sqrt{2.2}-1=2-1=1\)
c) \(A=B\Leftrightarrow\sqrt{2x}-1=2\Leftrightarrow\sqrt{2x}=3\)
\(\Leftrightarrow2x=9\Leftrightarrow x=\dfrac{9}{2}\left(tm\right)\)
