Đáp án:
x=24;y=3
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \pm y\\
\left\{ \begin{array}{l}
\frac{{108}}{{x + y}} + \frac{{63}}{{x - y}} = \frac{{81}}{{x + y}} + \frac{{84}}{{x - y}}\\
\frac{{81}}{{x + y}} + \frac{{84}}{{x - y}} = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\frac{{27}}{{x + y}} = \frac{{21}}{{x - y}}\\
\frac{{81}}{{x + y}} + \frac{{84}}{{x - y}} = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
27x - 27y = 21x + 21y\\
\frac{{81}}{{x + y}} + \frac{{84}}{{x - y}} = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
6x - 48y = 0\\
\frac{{81}}{{x + y}} + \frac{{84}}{{x - y}} = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 8y\\
\frac{{81}}{{8y + y}} + \frac{{84}}{{8y - y}} = 7\left( * \right)
\end{array} \right.\\
\left( * \right) \to \frac{{81}}{{9y}} + \frac{{84}}{{7y}} = 7\\
\to \frac{9}{y} + \frac{{12}}{y} = 7\\
\to 9 + 12 = 7y\\
\to y = 3 \to x = 24
\end{array}\)
