Đáp án:
Giải thích các bước giải:
$A=(\frac{x+2}{x-1}-\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{1}{1+\sqrt{x}}).(\frac{x\sqrt{x}-1}{\sqrt{x}-1}+\sqrt{x})$
$A=(\frac{x+2}{(\sqrt{x}-1)(\sqrt{x}+1)}-\frac{\sqrt{x}(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}=1)}+\frac{\sqrt{x}-1}{(1+\sqrt{x})(\sqrt{x}-1)}).(\frac{x\sqrt{x}-1}{\sqrt{x}-1}+\frac{x(\sqrt{x}-1)}{\sqrt{x}-1})$
$A=(\frac{x+2}{(\sqrt{x}-1)(\sqrt{x}+1)}-\frac{x+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}+\frac{\sqrt{x}-1}{(1+\sqrt{x})(\sqrt{x}-1)}).(\frac{x\sqrt{x}-1}{\sqrt{x}-1}+\frac{x-\sqrt{x}}{\sqrt{x}-1})$
$A=\frac{x+2-(x+\sqrt{x})+(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{x\sqrt{x}-1+x-\sqrt{x}}{\sqrt{x}-1}$
$A=\frac{x+2-x-\sqrt{x}+\sqrt{x}-1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{(\sqrt{x})^3-1^3+\sqrt{x}(\sqrt{x}-1)}{\sqrt{x}-1}$
$A=\frac{1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{(\sqrt{x}-1)[(\sqrt{x})^2+\sqrt{x}+1)]+\sqrt{x}(\sqrt{x}-1)}{\sqrt{x-1}]}$
$A=\frac{1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{(\sqrt{x}-1)(x+\sqrt{x}+1+\sqrt{x})}{\sqrt{x-1}}$
$A=\frac{1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{(\sqrt{x}-1)(x+2\sqrt{x}+1)}{\sqrt{x-1}}$
$A=\frac{1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{(\sqrt{x}-1)(\sqrt{x}+1)^2}{\sqrt{x-1}}$
$A=\frac{\sqrt{x}+1}{\sqrt{x}-1}$
