$$
\begin{array}{l}
\text { 7. Let } M=\left\{x \left\lvert\, \frac{x-2}{3}+\frac{x-3}{2}=\frac{3}{x-2}+\frac{2}{x-3}\right.\right\}, \\
N=\left\{x \left\lvert\, \frac{x-6}{5}+\frac{x-5}{6}=\frac{5}{x-6}+\frac{6}{x-5}\right.\right\} .
\end{array}
$$

Find $M \cap N=$
$$
N i, 7. M \cap N=\{0\} \text{. }
$$

From the given information, we can solve for
$$
M=\left\{0,5, \frac{13}{5}\right\}, N=\left\{0,11, \frac{61}{11}\right\} .
$$