a) \(A=\left(\dfrac{1}{x+2\sqrt{x}}-\dfrac{1}{\sqrt{x}+2}\right):\dfrac{1-\sqrt{x}}{x+4\sqrt{x}+4}\)
\(A=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}+2\right)}-\dfrac{1}{\sqrt{x}+2}\right):\dfrac{1-\sqrt{x}}{\sqrt{x^2}+2.2\sqrt{x}+2^2}\)
\(A=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\right):\dfrac{1-\sqrt{x}}{\left(\sqrt{x}+2\right)^2}\)
\(A=\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}:\dfrac{1-\sqrt{x}}{\left(\sqrt{x}+2\right)^2}\)
\(A=\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{1-\sqrt{x}}\)
\(A=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)
b) \(A=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)
\(\Rightarrow\dfrac{\sqrt{x}+2}{\sqrt{x}}=\dfrac{5}{3}\)
\(\Rightarrow3\left(\sqrt{x}+2\right)=5\sqrt{x}\)
\(\Rightarrow3\sqrt{x}+6-5\sqrt{x}=0\)
\(\Rightarrow-2\sqrt{x}=-6\)
\(\Rightarrow\sqrt{x}=3\)
\(\Rightarrow x=9\)
