Đáp án+Giải thích các bước giải:
\(F=(\dfrac{\sqrt{x}-\sqrt{y}}{x-y} +\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}})÷ \dfrac{\sqrt{xy}+1}{\sqrt{x}+\sqrt{y}}\\(x\ge 0,\quad y\ge 0, \quad x\ne y)\\F=(\dfrac{\sqrt{x}-\sqrt{y}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})} +\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}})÷ \dfrac{\sqrt{xy}+1}{\sqrt{x}+\sqrt{y}} \\F=(\dfrac{1}{\sqrt{x}+\sqrt{y}} +\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}})÷ \dfrac{\sqrt{xy}+1}{\sqrt{x}+\sqrt{y}}\\F=\dfrac{1+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}÷ \dfrac{\sqrt{xy}+1}{\sqrt{x}+\sqrt{y}}\\F=1\\G = \dfrac{x}{\sqrt{xy}+y} +\dfrac{y}{\sqrt{xy}+x}-\dfrac{x+y}{\sqrt{xy}}\\(xy\ge0,\quad x\ne y)\\G = \dfrac{x\sqrt{xy}(\sqrt{xy}+x)(+y\sqrt{xy}(\sqrt{xy}+y)-(\sqrt{xy}+y)(\sqrt{xy}+x)(x+y)}{\sqrt{xy}(\sqrt{xy}+y)(\sqrt{xy}+x)}\\G = \dfrac{-x^2y -xy^2 -2xy\sqrt{xy}}{\sqrt{xy}\sqrt{y}(\sqrt{x}+\sqrt{y})\sqrt{x}(\sqrt{y}+\sqrt{x})}\\G = \dfrac{-xy(x+y+2\sqrt{xy})}{\sqrt{xy}\sqrt{y}(\sqrt{x}+\sqrt{y})\sqrt{x}(\sqrt{y}+\sqrt{x})}\\G = \dfrac{-xy(\sqrt{x}+\sqrt{y})^2}{\sqrt{xy}\sqrt{y}(\sqrt{x}+\sqrt{y})\sqrt{x}(\sqrt{y}+\sqrt{x})}\\G =\dfrac{-xy}{\sqrt{xy}\sqrt{y}\sqrt{x}}\\G =\dfrac{-xy}{\sqrt{x^2y^2}}\\G=\dfrac{-xy}{xy}\\G =-1\\H =\dfrac{a-b}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\\(a\ge0,\quad b\ge 0,\quad a\ne b)\\H=\sqrt{a}+\sqrt{b}-\dfrac{a\sqrt{a}-b\sqrt{b}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}\\H=\sqrt{a}+\sqrt{b}-\dfrac{(\sqrt{a}-\sqrt{b})(a+\sqrt{ab}+b)}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}\\H=\sqrt{a}+\sqrt{b}-\dfrac{a+\sqrt{ab}+b}{\sqrt{a}+\sqrt{b}}\\H = \dfrac{(\sqrt{a}+\sqrt{b})\sqrt{a}+(\sqrt{a}+\sqrt{b})\sqrt{b}-(a+\sqrt{ab}+b)}{\sqrt{a}+\sqrt{b}}\\H =\dfrac{a+\sqrt{ab}+\sqrt{ab}+b-a-\sqrt{ab}-b}{\sqrt{a}+\sqrt{b}}\\H =\dfrac{\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)
