a) $P=1:\Bigg[\dfrac{x+2+(\sqrt[]{x}+1)(\sqrt[]{x}-1)}{(\sqrt[]{x}-1)(x+\sqrt[]{x}+1)}-\dfrac{\sqrt[]{x}+1}{(\sqrt[]{x}+1)(\sqrt[]{x}-1)}\Bigg]$
$=1:\Bigg[\dfrac{2x+1}{(\sqrt[]{x}-1)(x+\sqrt[]{x}+1)}-\dfrac{1}{\sqrt[]{x}-1}\Bigg]$
$=1:\Bigg[\dfrac{2x+1-(x+\sqrt[]{x}+1)}{(\sqrt[]{x}-1)(x+\sqrt[]{x}+1))}\Bigg]$
$=1:\Bigg[\dfrac{\sqrt[]{x}(\sqrt[]{x}-1)}{(\sqrt[]{x}-1)(x+\sqrt[]{x}+1)}\Bigg]$
$=1:\dfrac{\sqrt[]{x}}{x+\sqrt[]{x}+1}$
$=\dfrac{x+\sqrt[]{x}+1}{\sqrt[]{x}}$
b) $P=\dfrac{x+\sqrt[]{x}+1}{\sqrt[]{x}}$
$=\sqrt[]{x}+\dfrac{1}{\sqrt[]{x}}+1$
$≥2\sqrt[]{\sqrt[]{x}.\dfrac{1}{\sqrt[]{x}}}+1$
$=3$
Vậy $P≥3$
