1. Solve the inequality

$$
\frac{x^{2}-4 x+4}{x^{2}-6 x+9}+\frac{x-2}{x-3}-12<0
$$

in the set of real numbers $\mathbb{R}$
Solution. The inequality reduces to the inequality $\left(\frac{x-2}{x-3}\right)^{2}-\frac{x-2}{x-3}-120
\end{aligned}
$$

The set of solutions to inequality (1) is $(-\infty, 3) \cup\left(\frac{7}{2},+\infty\right)$, and the set of solutions to inequality (2) is $\left(-\infty, \frac{14}{5}\right) \cup(3,+\infty)$. Therefore, the set of solutions to the given inequality is $\left(-\infty, \frac{14}{5}\right) \cup\left(\frac{7}{2},+\infty\right)$.