\(A=\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)^2}=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
\(B=\dfrac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\left(\sqrt{x}-\sqrt{y}\right)^2}=\dfrac{\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\)
\(C=\dfrac{2\sqrt{a}-2a+\sqrt{a}-1}{\left(2\sqrt{a}-1\right)^2}=\dfrac{2\sqrt{a}\left(1-\sqrt{a}\right)-\left(1-\sqrt{a}\right)}{\left(2\sqrt{a}-1\right)^2}\)
\(=\dfrac{\left(1-\sqrt{a}\right)\left(2\sqrt{a}-1\right)}{\left(2\sqrt{a}-1\right)^2}=\dfrac{1-\sqrt{a}}{2\sqrt{a}-1}\)