6:
\(P=\dfrac{x-2\sqrt{x}+2\sqrt{x}+4}{x-4}\cdot\dfrac{\sqrt{x}+2}{x+4}\)
\(=\dfrac{x+4}{x+4}\cdot\dfrac{\sqrt{x}+2}{x-4}=\dfrac{1}{\sqrt{x}-2}\)
5:
\(Q=\left(\dfrac{a}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{a}{\sqrt{a}-2}\right)\cdot\dfrac{\left(\sqrt{a}-2\right)^2}{\sqrt{a}+1}\)
\(=\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\cdot\dfrac{\left(\sqrt{a}-2\right)^2}{\sqrt{a}-2}=\sqrt{a}\left(\sqrt{a}-2\right)\)
4:
\(P=\dfrac{\sqrt{2x}\cdot\sqrt{x}}{\sqrt{2x}\left(\sqrt{x}+\sqrt{2}\right)}+\dfrac{\sqrt{2}\left(\sqrt{x}-\sqrt{2}\right)}{x-2}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{2}}+\dfrac{\sqrt{2}}{\sqrt{x}+\sqrt{2}}=1\)
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