Question

 Rút gọn ( với các biểu thức đã có nghĩa )

a)\(\left[\dfrac{\left(\sqrt{x}+\sqrt{y}\right)^2-4\sqrt{xy}}{x-\sqrt{xy}}-2\right].\dfrac{\sqrt{x^3}-y\sqrt{x}}{\sqrt{x}+\sqrt{y}}\)

b)\(\left(\dfrac{a\sqrt{a}-m\sqrt{m}}{\sqrt{a}-\sqrt{m}}+\sqrt{am}\right).\left(\dfrac{\sqrt{a}-\sqrt{m}}{a-m}\right)^2\)

Answer 1

\(\text{a},=\left[\dfrac{x+2\sqrt{xy}+y-4\sqrt{xy}-2x+2\sqrt{xy}}{x-\sqrt{xy}}\right].\dfrac{\sqrt{x}\left(x-y\right)}{\sqrt{x}+\sqrt{y}}=\left(\dfrac{-x+y}{x-\sqrt{xy}}\right).\dfrac{\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)}{1}=\dfrac{-x+y}{x-\sqrt{xy}}.\dfrac{x-\sqrt{xy}}{1}=-x+y\\ b=\left(\dfrac{\sqrt{\text{a}^3}-\sqrt{m^3}}{\sqrt{\text{a}}-\sqrt{m}}+\sqrt{\text{a}m}\right).\left(\dfrac{1}{\sqrt{\text{a}}+\sqrt{m}}\right)^2=\left(\text{a}+\sqrt{\text{a}m}+m+\sqrt{\text{a}m}\right).\dfrac{1}{\left(\sqrt{\text{a}}+\sqrt{m}\right)^2}=\dfrac{\left(\sqrt{\text{a}}+\sqrt{m}\right)^2}{\left(\sqrt{\text{a}}+\sqrt{m}\right)^2}=1\)

Answer 2

`a)[[(\sqrt{x}+\sqrt{y})^2-4\sqrt{xy}]/[x-\sqrt{xy}]-2].[\sqrt{x^3}-y\sqrt{x}]/[\sqrt{x}+\sqrt{y}]`

`=([x+2\sqrt{xy}+y-4\sqrt{xy}]/[\sqrt{x}(\sqrt{x}-\sqrt{y})]-2].[\sqrt{x}(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})]/[\sqrt{x}+\sqrt{y}]`

`=([(\sqrt{x}-\sqrt{y})^2]/[\sqrt{x}(\sqrt{x}-\sqrt{y})]-2].[\sqrt{x}(\sqrt{x}-\sqrt{y})]`

`=[\sqrt{x}-\sqrt{y}-2\sqrt{x}]/\sqrt{x} .[\sqrt{x}(\sqrt{x}-\sqrt{y}]`

`=[-(\sqrt{x}+\sqrt{y})].(\sqrt{x}-\sqrt{y})=-(x-y)=y-x`

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`b)([a\sqrt{a}-m\sqrt{m}]/[\sqrt{a}-\sqrt{m}]+\sqrt{am}).([\sqrt{a}-\sqrt{m}]/[a-m])^2`

`=([(\sqrt{a}-\sqrt{m})(a+\sqrt{am}+m)]/[\sqrt{a}-\sqrt{m}]+\sqrt{am}).([\sqrt{a}-\sqrt{m}]/[(\sqrt{a}-\sqrt{m})(\sqrt{a}+\sqrt{m})])^2`

`=(a+\sqrt{am}+m+\sqrt{am}).(1/[\sqrt{a}+\sqrt{m}])^2`

`=(\sqrt{a}+\sqrt{m})^2 . 1/[(\sqrt{a}+\sqrt{m})^2]=1`