\(a,ĐK:\hept{\begin{cases}x\ge0\\\sqrt{x}+2\ne0\\\sqrt{x}-2\ne0;4-x\ne0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x\ge0\\x\ne4\end{cases}}\)
Rút gọn :
\(A=\frac{4}{\sqrt{x}+2}+\frac{2}{\sqrt{x}-2}+\frac{5\sqrt{x}-6}{4-x}\)
\(A=\frac{4}{\sqrt{x}+2}+\frac{2}{\sqrt{x}-2}-\frac{5\sqrt{x}-6}{x-4}\)
\(A=\frac{4\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\frac{2\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\frac{5\sqrt{x}-6}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(A=\frac{4\sqrt{x}-8+2\sqrt{x}+4-5\sqrt{x}+6}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(A=\frac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(A=\frac{1}{\sqrt{x}-2}\)
\(b,\)Để A nhận giá tri nguyên \(\Leftrightarrow\frac{1}{\sqrt{x}-2}\) nguyên
\(\Leftrightarrow\sqrt{x}-2\inƯ\left(1\right)\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}-2=1\\\sqrt{x}-2=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}\sqrt{x}=3\\\sqrt{x}=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=9\\x=1\end{cases}}}\)
Vậy A có giá tri nguyên \(\Leftrightarrow x\in\left\{1;9\right\}\)
