The following expressions should be simplified to their simplest form:

$$
\begin{gathered}
\frac{12 a^{3} x^{4}+2 a^{2} x^{5}}{18 a b^{2} x+3 b^{2} x^{2}}, \frac{4-2 x+x^{2}}{x+2}-x-2 \\
\frac{1}{(a-b)(a-c)}+\frac{1}{(b-a)(b-c)}+\frac{1}{(c-a)(c-b)}
\end{gathered}
$$
$$
\begin{gathered}
\frac{12 a^{3} x^{4}+2 a^{2} x^{5}}{18 a b^{2} x+3 b^{2} x^{2}}=\frac{2 a^{2} x^{4}(6 a+x)}{3 b^{2} x(6 a+x)}=\frac{2 a^{2} x^{3}}{3 b^{2}} \\
\frac{4-2 x+x^{2}}{x+2}-x-2=\frac{4-2 x+x^{2}-x^{2}-4 x-4}{x+2}=-\frac{6 x}{x+2} \\
\frac{1}{(a-b)(a-c)}+\frac{1}{(b-a)(b-c)}+\frac{1}{(c-a)(c-b)}= \\
=\frac{1}{(a-b)(a-c)}-\frac{1}{(b-a)(b-c)}+\frac{1}{(a-c)(b-c)}= \\
=\frac{b-c-a+c+a-b}{(a-b)(a-c)(b-c)}=0
\end{gathered}
$$

(Jeno Klein, Budapest.)