What is the value of the following fraction:

$1234321234321 \cdot 2468642468641-1234321234320$

$\overline{1234321234320 \cdot 2468642468641+1234321234321}$.
Notice that all occurring numbers can be easily expressed, for example, by the second term of the numerator. $1234321234320=$ with the notation $a$, the value of the fraction is:

$$
\frac{(a+1)(2 a+1)-a}{a(2 a+1)+(a+1)}=\frac{2 a^{2}+2 a+1}{2 a^{2}+2 a+1}=1
$$

(Thus, it would be unnecessary to carry out the lengthy operations.)

Zsuzsa Kopcsányi (Budapest, Berzsenyi D. Ig. I. o.t.)