Giải thích các bước giải:
\(\begin{array}{l}
a.A = \left[ {\frac{{4\sqrt x + 2 + 3\sqrt x - 6 - 5\sqrt x + 7}}{{\left( {\sqrt x - 2} \right)\left( {2\sqrt x + 1} \right)}}} \right].\frac{{5\sqrt x \left( {\sqrt x - 2} \right)}}{{2\sqrt x + 3}}\\
= \frac{{2\sqrt x + 3}}{{\left( {\sqrt x - 2} \right)\left( {2\sqrt x + 1} \right)}}.\frac{{5\sqrt x \left( {\sqrt x - 2} \right)}}{{2\sqrt x + 3}}\\
= \frac{{5\sqrt x }}{{2\sqrt x + 1}}\\
b.A \in Z \to 2A \in Z\\
\to \frac{{10\sqrt x }}{{2\sqrt x + 1}} \in Z\\
\to \frac{{10\sqrt x }}{{2\sqrt x + 1}} = \frac{{5\left( {2\sqrt x + 1} \right) - 5}}{{2\sqrt x + 1}} = 5 - \frac{5}{{2\sqrt x + 1}} \in Z\\
\to \frac{5}{{2\sqrt x + 1}} \in Z\\
\to 2\sqrt x + 1 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
2\sqrt x + 1 = 5\\
2\sqrt x + 1 = - 5\\
2\sqrt x + 1 = 1\\
2\sqrt x + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 4\left( l \right)\\
\sqrt x = - 3\left( l \right)\\
x = 0\left( l \right)\\
\sqrt x = - 1\left( l \right)
\end{array} \right.
\end{array}\)
⇒ Không tồn tại giá trị x TMĐK
