$(\dfrac{\sqrt[]{x}+2}{x+2\sqrt[]{x}+1}-$ $\dfrac{\sqrt[]{x}-2}{x-1}).$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$=(\dfrac{\sqrt[]{x}+2}{(\sqrt[]{x}+1)^2}-$ $\dfrac{\sqrt[]{x}-2}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}).$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$=\dfrac{(\sqrt[]{x}+2)(\sqrt[]{x}-1)-(\sqrt[]{x}-2)(\sqrt[]{x}+1)}{(\sqrt[]{x}+1)^2.(\sqrt[]{x}-1)}.$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$\dfrac{x-\sqrt[]{x}+2\sqrt[]{x}-2-(x+\sqrt[]{x}-2\sqrt[]{x}-2)}{(\sqrt[]{x}+1)^2.(\sqrt[]{x}-1)}.$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$=\dfrac{x+\sqrt[]{x}-2-x+\sqrt[]{x}+2}{(\sqrt[]{x}+1)^2.(\sqrt[]{x}-1)}.$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$=\dfrac{2\sqrt[]{x}}{(\sqrt[]{x}+1)^2.(\sqrt[]{x}-1)}.$ $\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}}$
$=\dfrac{2(\sqrt[]{x}+1)}{(\sqrt[]{x}+1)^2.(\sqrt[]{x}-1)}$
$=\dfrac{2}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$
$=\dfrac{2}{x-1}$
Chúc bạn học tốt !!!!
