1.26/
a/ ĐKXĐ: $x>0,x\ne 1$
$B\,=\left(\dfrac{1}{x-\sqrt x}+\dfrac{1}{\sqrt x-1}\right):\dfrac{\sqrt x+1}{(\sqrt x-1)^2}\\\quad =\left(\dfrac{1}{\sqrt x(\sqrt x-1)}+\dfrac{\sqrt x}{\sqrt x(\sqrt x-1)}\right).\dfrac{(\sqrt x-1)^2}{\sqrt x+1}\\\quad =\dfrac{1+\sqrt x}{\sqrt x(\sqrt x-1)}.\dfrac{(\sqrt x-1)^2}{\sqrt x+1}\\\quad =\dfrac{\sqrt x-1}{\sqrt x}$
Vậy $B=\dfrac{\sqrt x-1}{\sqrt x}$ với $x>0,x\ne 1$
b/ $\dfrac{B}{A}\,=\dfrac{\dfrac{\sqrt x-1}{\sqrt x}}{\dfrac{\sqrt x-1}{\sqrt x+1}}\\\quad =\dfrac{\sqrt x-1}{\sqrt x}:\dfrac{\sqrt x-1}{\sqrt x+1}\\\quad =\dfrac{\sqrt x-1}{\sqrt x}.\dfrac{\sqrt x+1}{\sqrt x-1}\\\quad =\dfrac{\sqrt x+1}{\sqrt x}$
$\dfrac{B}{A}=\dfrac{4}{3}\\↔\dfrac{\sqrt x+1}{\sqrt x}=\dfrac{4}{3}\\↔\dfrac{3(\sqrt x+1)}{3\sqrt x}=\dfrac{4\sqrt x}{3\sqrt x}\\→3\sqrt x+3=4\sqrt x\\↔-\sqrt x=-3\\↔\sqrt x=3\\↔x=9(TM)$
Vậy $x=9$ thì $\dfrac{B}{A}=\dfrac{4}{3}$
1.27/
1) $A\,=\left(\sqrt{12}-2\sqrt 3+5\sqrt 2-\dfrac{3}{4}\sqrt 8\right).(2\sqrt 6)\\\quad =\left(\sqrt{4.3}-2\sqrt 3+5\sqrt 2-\dfrac{3}{4}\sqrt{4.2}\right).2\sqrt 6\\\quad =\left(2\sqrt 3-2\sqrt 3+5\sqrt 2-\dfrac{3}{2}\sqrt 2\right).2\sqrt 6\\\quad =\dfrac{7}{2}\sqrt 2.2\sqrt 6\\\quad =14\sqrt 3$
Vậy $A=14\sqrt 3$
2) a
a/ ĐKXĐ: $x>0,x\ne 1,x\ne 4$
$B\,=\left(1-\dfrac{4\sqrt x}{x-1}+\dfrac{1}{\sqrt x-1}\right):\dfrac{x-2\sqrt x}{x-1}\\\quad =\left(\dfrac{(\sqrt x-1)(\sqrt x+1)}{(\sqrt x-1)(\sqrt x+1)}-\dfrac{4\sqrt x}{(\sqrt x-1)(\sqrt x+1)}+\dfrac{\sqrt x+1}{(\sqrt x-1)(\sqrt x+1)}\right):\dfrac{\sqrt x(\sqrt x-2)}{(\sqrt x-1)(\sqrt x+1)}\\\quad =\dfrac{x-1-4\sqrt x+\sqrt x+1}{(\sqrt x-1)(\sqrt x+1)}.\dfrac{(\sqrt x-1)(\sqrt x+1)}{\sqrt x(\sqrt x-2)}\\\quad =\dfrac{x-3\sqrt x}{1}.\dfrac{1}{\sqrt x(\sqrt x-2)}\\\quad =\dfrac{\sqrt x(\sqrt x-3)}{\sqrt x(\sqrt x-2)}\\\quad =\dfrac{\sqrt x-3}{\sqrt x-2}$
Vậy $B=\dfrac{\sqrt x-3}{\sqrt x-2}$ với $x>0,x\ne 1,x\ne 4$
b/ $B=\dfrac{1}{2}\\↔\dfrac{\sqrt x-3}{\sqrt x-2}=\dfrac{1}{2}\\↔\dfrac{2(\sqrt x-3)}{2(\sqrt x-2)}=\dfrac{\sqrt x-2}{2(\sqrt x-2)}\\→2\sqrt x-6=\sqrt x-2\\↔\sqrt x=4\\↔x=16(TM)$
Vậy $B=\dfrac{1}{2}$ thì $x=16$
