Rút gọn bài 9 câu a tớ cần gấp

Giải thích các bước giải:

Ta có:

$P=(\dfrac1{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}-x+\sqrt{x}-1}):(\dfrac{x+\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}+\dfrac1{x+1})$ 

$\to P=(\dfrac1{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{(\sqrt{x}-1)(x+1)}):(\dfrac{\sqrt{x}(\sqrt{x}+1)}{(x+1)(\sqrt{x}+1)}+\dfrac1{x+1})$

$\to P=\dfrac{x+1-2\sqrt{x}}{(\sqrt{x}-1)(x+1)}:(\dfrac{\sqrt{x}}{x+1}+\dfrac1{x+1})$

$\to P=\dfrac{(\sqrt{x}-1)^2}{(\sqrt{x}-1)(x+1)}:\dfrac{\sqrt{x}+1}{x+1}$

$\to P=\dfrac{\sqrt{x}-1}{x+1}\cdot\dfrac{x+1}{\sqrt{x}+1}$

$\to P=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}$