Question

Answer 1

\(M=\left(\dfrac{\sqrt{x}+2}{x-2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right):\dfrac{2\sqrt{x}}{x-1}\left(đk:x>0,x\ne1\right)\)

\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{\left(x-1\right)\left(\sqrt{x}-1\right)}.\dfrac{x-1}{2\sqrt{x}}=\dfrac{x+3\sqrt{x}+2-x+3\sqrt{x}-2}{2\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{6\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{3}{\sqrt{x}-1}\)