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