B1: Cho P = ($\sqrt{x}$ + $\frac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}$ ) : ($\frac{x}{\sqrt{xy}+y}$ + $\frac{y}{\sqrt{xy}-y}$ – $\frac{x+y}{\sqrt{xy}}$) a,

Đáp án:

B1

a, $P= \sqrt{y}-\sqrt{x}$

b, 1

B2 : $= 3\left ( \sqrt{x}-1-\sqrt{3} \right )\left ( \sqrt{x}-1+\sqrt{3} \right )$

Giải thích các bước giải: 

a,

$P= \left [ \sqrt{x}+\dfrac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}} \right ]:\left [ \dfrac{x}{\sqrt{xy}+y}+\dfrac{y}{\sqrt{xy}-x} -\dfrac{x-y}{\sqrt{xy}}\right ]$
$P= \dfrac{\sqrt{x}\left ({\sqrt{x}+\sqrt{y}} \right )+y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left [ \dfrac{x}{\sqrt{y}\left ( \sqrt{x}+\sqrt{y} \right )} +\dfrac{y}{\sqrt{x}\left ( \sqrt{y}-\sqrt{x} \right )}-\dfrac{x+y}{\sqrt{xy}} \right ]$
$P= \dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\left [ \dfrac{x\sqrt{x}\left ( \sqrt{y}-\sqrt{x} \right )+y\sqrt{y}\left ( \sqrt{x}+\sqrt{y} \right )-\left ( x+y \right )\left ( \sqrt{x}+\sqrt{y} \right )\left ( \sqrt{y}-\sqrt{x} \right )}{\sqrt{xy}\left ( \sqrt{x}+\sqrt{y} \right )\left ( \sqrt{y}-\sqrt{x} \right )} \right ]$
$P= \dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\left [ \dfrac{x\sqrt{xy}-x^{2}+y\sqrt{xy}+y^{2}-\left ( x+y \right )\left ( y-x \right )}{\sqrt{xy}\left ( \sqrt{x}+\sqrt{y} \right )\left ( \sqrt{y}-\sqrt{x} \right )} \right ]$
$P= \dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\dfrac{x\sqrt{xy}+y\sqrt{xy}}{\sqrt{xy}\left ( \sqrt{x}+\sqrt{y} \right )\left ( \sqrt{y}-\sqrt{x} \right )}$
$P= \dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\dfrac{\sqrt{xy}\left ( x+y \right )}{\sqrt{xy}\left ( \sqrt{x}+\sqrt{y} \right )\left ( \sqrt{y}-\sqrt{x} \right )}$
$P= \sqrt{y}-\sqrt{x}$

b, 

$x= 3,y= 4+2\sqrt{3}$
$\Rightarrow P= \sqrt{4+2\sqrt{3}}-\sqrt{3}$
             $= \sqrt{\left ( \sqrt{3}+1 \right )^{2}}-\sqrt{3}$
             $= \sqrt{3}+1-\sqrt{3}= 1$

B2:

$3x-6\sqrt{x}-6$
$= 3\left ( x-2\sqrt{x}-2 \right )$
$= 3\left ( x-2\sqrt{x}+1-3 \right )$
$= 3\left ( \left ( \sqrt{x}-1 \right )^{2}-3 \right )$
$= 3\left ( \sqrt{x}-1-\sqrt{3} \right )\left ( \sqrt{x}-1+\sqrt{3} \right )$