Đáp án:
\[A = 8\]
Giải thích các bước giải:
Đặt \(\dfrac{x}{3} = \dfrac{y}{5} = k\), ta có:
\(\begin{array}{l}
\dfrac{x}{3} = \dfrac{y}{5} = k \Rightarrow \left\{ \begin{array}{l}
x = 3k\\
y = 5k
\end{array} \right.\\
A = \dfrac{{5{x^2} + 3{y^2}}}{{10{x^2} - 3{y^2}}} = \dfrac{{5.{{\left( {3k} \right)}^2} + 3.{{\left( {5k} \right)}^2}}}{{10.{{\left( {3k} \right)}^2} - 3.{{\left( {5k} \right)}^2}}}\\
= \dfrac{{5.9{k^2} + 3.25{k^2}}}{{10.9{k^2} - 3.25{k^2}}} = \dfrac{{45{k^2} + 75{k^2}}}{{90{k^2} - 75{k^2}}}\\
= \dfrac{{120{k^2}}}{{15{k^2}}} = \dfrac{{120}}{{15}} = 8
\end{array}\)
Vậy \(A = 8\)
