Đáp án:
\[\frac{{13}}{2}\]
Giải thích các bước giải:
Đặt \[\begin{array}{l}
\frac{{9x}}{4} = \frac{{4y}}{3} = \frac{{12z}}{5} = t\\
\Rightarrow \left\{ \begin{array}{l}
9x = 4t\\
4y = 3t\\
12z = 5t
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \frac{{4t}}{9}\\
y = \frac{{3t}}{4}\\
z = \frac{{5t}}{{12}}
\end{array} \right.\\
A = \frac{{y + z - x}}{{x - y + z}} = \frac{{\frac{{3t}}{4} + \frac{{5t}}{{12}} - \frac{{4t}}{9}}}{{\frac{{4t}}{9} - \frac{{3t}}{4} + \frac{{5t}}{{12}}}} = \frac{{t\left( {\frac{3}{4} + \frac{5}{{12}} - \frac{4}{9}} \right)}}{{t\left( {\frac{4}{9} - \frac{3}{4} + \frac{5}{{12}}} \right)}} = \frac{{13}}{2}
\end{array}\]
