$\begin{array}{l}
A = \dfrac{{34}}{{x - 4\sqrt {x - 3} + 9}} = \dfrac{{34}}{{x - 3 - 4\sqrt {x - 3} + 4 + 8}} = \dfrac{{34}}{{{{\left( {\sqrt {x - 3} - 2} \right)}^2} + 8}}\\
{\left( {\sqrt {x - 3} - 2} \right)^2} + 8 \ge 8 \Rightarrow A \le \dfrac{{34}}{8} = \dfrac{{17}}{4} \Rightarrow \max A = \dfrac{{17}}{4}\\
' = ' \Leftrightarrow \sqrt {x - 3} = 2 \Leftrightarrow x - 3 = 4 \Leftrightarrow x = 7
\end{array}$
