Rút gọn( giả sử mọi đkiện thỏa mãn: (√(2x+1)/(√(x^3 )-1) - √x/(x+1+√x) ) . ( (1+√(x^3 ))/(1+√x) - √x). giúp e với ạ
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Ta co
$(\dfrac{\sqrt{2x+1}}{\sqrt{x^3}-1} - \dfrac{\sqrt{x}}{x + 1 + \sqrt{x}}) .(\dfrac{1 + \sqrt{x^3}}{1 + \sqrt{x}} - \sqrt{x})$
$= (\dfrac{\sqrt{2x+1}}{\sqrt{x^3}-1} - \dfrac{\sqrt{x}(\sqrt{x}-1)}{(\sqrt{x}-1)(x + 1 + \sqrt{x}}) .(\dfrac{(1 + \sqrt{x})(x - \sqrt{x}+1)}{1 + \sqrt{x}} - \sqrt{x})$
$= \dfrac{\sqrt{2x+1} - (x-\sqrt{x})}{\sqrt{x^3}-1} . (x - 2\sqrt{x} + 1)$
$= \dfrac{\sqrt{2x+1} - x+\sqrt{x}}{(\sqrt{x} - 1)(x + \sqrt{x} + 1)} . (\sqrt{x}-1)^2$
$= \dfrac{\sqrt{2x+1} - x+\sqrt{x}}{x + \sqrt{x} + 1} . (\sqrt{x}-1)$
