Ta có \(A=\left(\frac{2\sqrt{xy}}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}+\frac{\sqrt{x}-\sqrt{y}}{2\left(\sqrt{x}+\sqrt{y}\right)}\right)\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\frac{\sqrt{y}}{\sqrt{y}-\sqrt{x}}\)

         \(=\left(\frac{4\sqrt{xy}+\left(\sqrt{x}-\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right)\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)                 (Quy đồng biểu thức đầu và đổi dấu số hạng cuối)

         \(=\left(\frac{4\sqrt{xy}+x-2\sqrt{xy}+y}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right)\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)

           \(=\frac{\left(\sqrt{x}+\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)

          \(=\frac{\sqrt{x}+\sqrt{y}}{2\left(\sqrt{x}-\sqrt{y}\right)}\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{\sqrt{x}}{\sqrt{x}-\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}=1.\)

Vậy giá trị biểu thức \(A=1.\)

\(=\frac{\left(\sqrt{x}+\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\cdot\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)

bài này dài lắm mk ko tiện làm

a) ĐK : tự ghi nha

b)

\(Q=\left(\frac{2\sqrt{xy}}{x-y}-\frac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}-2\sqrt{y}}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=\left(\frac{4\sqrt{xy}}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}-\frac{\left(\sqrt{x}+\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=\left(\frac{4\sqrt{xy}-\left(\sqrt{x}+\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=\left(\frac{4\sqrt{xy}-\left(x+y+2\sqrt{xy}\right)}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=\left(\frac{4\sqrt{xy}-x-y-2\sqrt{xy}}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=\left(\frac{2\sqrt{xy}-x-y}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=-\left(\frac{x-2\sqrt{xy}+y}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=-\left(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=-\left(\frac{\sqrt{x}-\sqrt{y}}{2\left(\sqrt{x}+\sqrt{y}\right)}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(Q=-\frac{1}{2\left(\sqrt{x}+\sqrt{y}\right)}.2\sqrt{x}\)

\(Q=-\frac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}\)

P /s : Các bạn tham khảo nhé

Bạn đung phương pháp nhân liên hợp nha bạn

nhân liên hợp là thế nào ?

cái Google sinh ra chỉ để bạn lên đây thôi ak

$\left(x^{\sqrt{2}}y\right)^{\sqrt{2}} = x^{\sqrt{2} \cdot \sqrt{2}}y^{\sqrt{2}} = x^2y^{\sqrt{2}}$

$x^2y^{\sqrt{2}} \cdot 9y^{-\sqrt{2}} = 9x^2y^{\sqrt{2}}y^{-\sqrt{2}} = 9x^2$

\(=\dfrac{xy\left(x^{\dfrac{1}{2}}+y^{\dfrac{1}{2}}\right)}{x^{\dfrac{1}{2}}+y^{\dfrac{1}{2}}}=xy\)

\(A=\dfrac{x^{\dfrac{3}{2}}y+xy^{\dfrac{3}{2}}}{\sqrt{x}+\sqrt{y}}=\left(x+y\right).\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\).

\(A=\left\{\frac{2\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+\sqrt{y}}+\frac{\sqrt{x}\left(x+y\right)}{\sqrt{x}}\right\}.\left(\frac{\sqrt{x}-\sqrt{y}}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}\right)^2.\)

=> \(A=\left(2\sqrt{xy}+x+y\right).\frac{1}{\left(\sqrt{x}+\sqrt{y}\right)^2}\)

=> \(A=\frac{\left(\sqrt{x}+\sqrt{y}\right)^2}{\left(\sqrt{x}+\sqrt{y}\right)^2}=1\)

ĐS: A=1

Sai đề