7B:
a: \(Q=\frac{x\sqrt{y}-y\cdot\sqrt{x}}{x-2\sqrt{xy}+y}\)
\(=\frac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\left(\sqrt{x}-\sqrt{y}\right)^2}=\frac{\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\)
b: \(P=\frac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\frac{4-a}{\sqrt{a}-2}\)
\(=\frac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}+2}-\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}-2}\)
\(=\sqrt{a}+2-\left(\sqrt{a}+2\right)=0\)
7A:
a: \(M=\frac{x\cdot\sqrt{y}+y\cdot\sqrt{x}}{x+2\sqrt{xy}+y}\)
\(=\frac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)^2}=\frac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
b: \(N=\frac{3\sqrt{a}-2a-1}{4a-4\sqrt{a}+1}\)
\(=\frac{-2a+2\sqrt{a}+\sqrt{a}-1}{\left(2\sqrt{a}-1\right)^2}=\frac{\left(\sqrt{a}-1\right)\left(-2\sqrt{a}+1\right)}{\left(-2\sqrt{a}+1\right)^2}\)
\(=\frac{\sqrt{a}-1}{-2\sqrt{a}+1}\)
