a) \(A=\left(\dfrac{\sqrt{x}+10}{x+\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{1+\sqrt{x}}{\sqrt{x}+2}\right):\dfrac{1}{\sqrt{x}-1}\)
\(=\left(\dfrac{\sqrt{x}+10}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{1+\sqrt{x}}{\sqrt{x}+2}\right).\left(\sqrt{x}-1\right)\)
\(=\dfrac{\sqrt{x}+10+\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(\sqrt{x}-1\right)\)
\(=\dfrac{\sqrt{x}+7}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(\sqrt{x}-1\right)=\dfrac{\sqrt{x}+7}{\sqrt{x}+2}\)
b) \(\sqrt{x}=\sqrt{3+2\sqrt{2}}=\sqrt{\left(\sqrt{2}+1\right)^2}=\sqrt{2}+1\)
\(\Rightarrow A=\dfrac{\sqrt{2}+1+7}{\sqrt{2}+1+2}=\dfrac{\sqrt{2}+8}{\sqrt{2}+3}\)
c) \(A=\dfrac{3}{2}\Rightarrow\dfrac{\sqrt{x}+7}{\sqrt{x}+2}=\dfrac{3}{2}\Rightarrow3\sqrt{x}+6=2\sqrt{x}+14\Rightarrow\sqrt{x}=8\)
\(\Rightarrow x=64\)
