Aprēḳināt izteiksmes \(\frac{20252024^{2}}{20252023^{2}+20252025^{2}-2}\) vērtību!
Apzīmējam \(20252024=a\), tad iegūstam, ka
\[\frac{20252024^{2}}{20252023^{2}+20252025^{2}-2} = \frac{a^{2}}{(a-1)^{2}+(a+1)^{2}-2},\]
\[\frac{a^{2}}{(a-1)^{2}+(a+1)^{2}-2} = \frac{a^{2}}{a^{2}-2 a+1+a^{2}+2 a+1-2} = \frac{1}{2}.\]