11: \(=\dfrac{-x+9+x-4\sqrt{x}+4+x-9}{x+\sqrt{x}-6}\)
\(=\dfrac{\left(\sqrt{x}-2\right)^2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\)
12: \(=\dfrac{\left(3-\sqrt{x}\right)\left(3\sqrt{x}-2\right)+\left(3\sqrt{x}+4\right)\left(5\sqrt{x}+7\right)-42\sqrt{x}-34}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}\)
\(=\dfrac{9\sqrt{x}-6-3x+2\sqrt{x}+15x+41\sqrt{x}+28-42\sqrt{x}-34}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}\)
\(=\dfrac{12x+10\sqrt{x}-12}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}\)
\(=\dfrac{12\sqrt{x}-8\sqrt{x}+18\sqrt{x}-12}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\)
13:
\(=\dfrac{2x+\sqrt{x}-6-3x+6\sqrt{x}+4\sqrt{x}-8-7\sqrt{x}+10}{\left(-\sqrt{x}+2\right)\left(2\sqrt{x}-3\right)}\)
\(=\dfrac{-x+4\sqrt{x}-4}{\left(-\sqrt{x}+2\right)\left(2\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}\)
