Đáp án:A$=\frac{-\sqrt{x}+3}{3\sqrt{x}-1}$
B$=-a+1$
C=-8
D$=\frac{-2}{\sqrt{a}+1}$
E$=\frac{2}{x+\sqrt{x}+1}$
Giải thích các bước giải:
$A=(\frac{1}{\sqrt{x}-1}-\frac{2}{\sqrt{x}+1}):\frac{3\sqrt{x}-1}{x-1} (x\neq1)$
$=\frac{\sqrt{x}+1-2(\sqrt{x}-1)}{x-1}·\frac{x-1}{3\sqrt{x}-1}$
$=\frac{-\sqrt{x}+3}{x-1}·\frac{x-1}{3\sqrt{x}-1}$
$=\frac{-\sqrt{x}+3}{3\sqrt{x}-1}$
$B=(1+\frac{a-\sqrt{a}}{\sqrt{a}-1})·(1-\frac{a+\sqrt{a}}{\sqrt{a}+1})$
$=(\frac{\sqrt{a}-1+a-\sqrt{a}}{\sqrt{a}-1})·\frac{\sqrt{a}+1-a-\sqrt{a}}{\sqrt{a}+1}$
$=\frac{a-1}{\sqrt{a}-1}·\frac{-a+1}{\sqrt{a}+1}$
$=-a+1$
$C=(\frac{\sqrt{x}-2}{\sqrt{x}+2}-\frac{\sqrt{x}+2}{\sqrt{x}-2})·(\sqrt{x}-\frac{4}{\sqrt{x}})$
$=\frac{x-4\sqrt{x}+4-x-4\sqrt{x}-4}{x-4}·\frac{x-4}{\sqrt{x}}$
$=\frac{-8\sqrt{x}}{x-4}·\frac{x-4}{\sqrt{x}}$
$=-8$
$D=(\frac{1}{1-\sqrt{a}}-\frac{1}{1+\sqrt{a}})·(1-\frac{1}{\sqrt{a}})$
$=(\frac{1+\sqrt{a}-1+\sqrt{a}}{1-a})·\frac{\sqrt{a}-1}{\sqrt{a}}$
$=\frac{-2\sqrt{a}}{(\sqrt{a}-1)(\sqrt{a}+1)}·\frac{\sqrt{a}-1}{\sqrt{a}}$
$=\frac{-2}{\sqrt{a}+1}$
$E=(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}:\frac{\sqrt{x}-1}{2}$
$=\frac{x+2}{(\sqrt{x}-1)(x+\sqrt{x}+1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}·\frac{2}{\sqrt{x}-1}$
$=\frac{x+2+\sqrt{x}(\sqrt{x}-1)-x-\sqrt{x}-1}{(\sqrt{x}-1)(x+\sqrt{x}+1}·\frac{2}{\sqrt{x}-1}$
$=\frac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{(\sqrt{x}-1)(x+\sqrt{x}+1}·\frac{2}{\sqrt{x}-1}$
$=\frac{x-2\sqrt{x}+1}{(\sqrt{x}-1)(x+\sqrt{x}+1}·\frac{2}{\sqrt{x}-1}$
$=\frac{(\sqrt{x}-1)^{2}}{(\sqrt{x}-1)(x+\sqrt{x}+1}·\frac{2}{\sqrt{x}-1}$
$=\frac{2}{x+\sqrt{x}+1}$
