Giải thích các bước giải:
a.$A=\dfrac{x+2}{(\sqrt{x}-1)(x+\sqrt{x}+1)}+\dfrac{\sqrt{x}.(\sqrt{x}-1)}{(\sqrt{x}-1)(x+\sqrt{x}+1)}-\dfrac{x+\sqrt{x}+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}$
$\rightarrow A=\dfrac{x+2+\sqrt{x}.(\sqrt{x}-1)+x+\sqrt{x}+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}$
$\rightarrow A=\dfrac{x+2+x-\sqrt{x}+x+\sqrt{x}+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}$
$\rightarrow A=\dfrac{3x+3}{(\sqrt{x}-1)(x+\sqrt{x}+1)}$
b.Ta có : $P=\dfrac{A}{B}=\dfrac{3x+3}{2(x+\sqrt{x}+1)}$
$\rightarrow P=\dfrac{3}{2}.\dfrac{x+1}{x+\sqrt{x}+1}$
$\rightarrow P=\dfrac{3}{2}.\dfrac{x+1}{x+1+\sqrt{x}}$
$\rightarrow P=\dfrac{3}{2}.(1-\dfrac{\sqrt{x}}{x+1+\sqrt{x}})$
$\rightarrow P\le \dfrac{3}{2}.(1-0)$
$\rightarrow P\le \dfrac{3}{2}$
$\rightarrow MaxP=\dfrac{3}{2}$
