a) \(A=\dfrac{2\sqrt{x}-x+2+\sqrt{x}+x+4}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}=\dfrac{3\left(2+\sqrt{x}\right)}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}=\dfrac{3}{2-\sqrt{x}}\)
b) \(A=\dfrac{3}{2-\sqrt{x}}>0\)
\(\Leftrightarrow2-\sqrt{x}>0\Leftrightarrow\sqrt{x}< 2\)
Do \(x\in Z^+,x\ne4\)
\(\Rightarrow x\in\left\{0;1;2;3\right\}\)


