Ответ:

[tex]\left\{\begin{array}{l}\dfrac{5}{3x-2y}+\dfrac{2}{2x+y}=21\\\dfrac{9}{3x-2y}+\dfrac{8}{2x+y}=40\end{array}\right\ \ ,\ \ \ \left\{\begin{array}{l}3x\ne 2y\\2x\ne -y\end{array}\right[/tex]

Выполним замену   [tex]u=\dfrac{1}{3x-2y}\ ,\ \ v=\dfrac{1}{2x+y}[/tex]  ,  тогда система примет вид

[tex]\left\{\begin{array}{l}5u+2v=21\Big|\cdot (-4)\\9u+8v=40\end{array}\right\ \oplus \ \left\{\begin{array}{l}5u+2v=21\\-11u=-44\end{array}\right\ \ \left\{\begin{array}{l}2v=21-5u\\u=4\end{array}\right[/tex]

Решаем систему методом сложения.

[tex]\left\{\begin{array}{l}2v=1\\u=4\end{array}\right\ \ \left\{\begin{array}{l}v=\dfrac{1}{2}\\u=4\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{1}{3x-2y}=4\\\dfrac{1}{2x+y}=\dfrac{1}{2}\end{array}\right\ \ \left\{\begin{array}{l}3x-2y=\dfrac{1}{4}\\2x+y=2\ \Big|\cdot 2\end{array}\right\ \oplus[/tex]

[tex]\left\{\begin{array}{l}7x=\dfrac{17}{4}\\y=2-2x\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{17}{28}\\y=2-\dfrac{34}{28}\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{17}{28}\\\ y=\dfrac{11}{14}\end{array}\right[/tex]

[tex]Otvet:\ \Big(\ \dfrac{17}{28}\ ;\ \dfrac{11}{14}\Big)\ .[/tex]