Giải thích các bước giải:

a.Ta có:

$A= (\dfrac{\sqrt{x}}{\sqrt{x}+2}+\dfrac{8\sqrt{x}+8}{x+2\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}}): (\dfrac{x+\sqrt{x}+3}{x+2\sqrt{x}}+\dfrac1{\sqrt{x}})$

$\to A=\dfrac{x+(8\sqrt{x}+8)-(\sqrt{x}+2)^2}{\sqrt{x}(\sqrt{x}+2)}: \dfrac{x+\sqrt{x}+3+\sqrt{x}+2}{\sqrt{x}(\sqrt{x}+2)}$

$\to A=\dfrac{4\sqrt{x}+4}{\sqrt{x}(\sqrt{x}+2)}: \dfrac{x+2\sqrt{x}+5}{\sqrt{x}(\sqrt{x}+2)}$

$\to A=\dfrac{4\sqrt{x}+4}{x+2\sqrt{x}+5}$

b.Ta có:

$A-1=\dfrac{4\sqrt{x}+4}{x+2\sqrt{x}+5}-1=\dfrac{-x+2\sqrt{x}-1}{x+2\sqrt{x}+5}=-\dfrac{(\sqrt{x}-1)^2}{(\sqrt{x}+1)^2+4}\le 0$

$\to A\le 1$