7: \(=\left(1+\sqrt{a}\right)\cdot\left(\dfrac{a\left(\sqrt{a}+1\right)+\sqrt{a}+1}{\sqrt{a}+1}-\sqrt{a}\right)\)
\(=\left(\sqrt{a}+1\right)\left(a+1-\sqrt{a}\right)=a\sqrt{a}+1\)
8: \(=\dfrac{3\sqrt{x}-x+x+9}{9-x}:\dfrac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3\left(\sqrt{x}+3\right)}{-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}\)
\(=\dfrac{-3\sqrt{x}}{2\sqrt{x}+4}\)