Zapišimo dani izraz bez negativnih eksponenata, a potencije s racionalnim eksponentima zapišimo pomoću korijena (ili obratno). Nakon toga ćemo primijeniti formule za kvadrat binoma i razliku kubova. Tada redom dobivamo:
1 ( 337 1 2 + 6 1 2 ) − 2 − ( 337 − 6 337 3 2 − 6 3 2 ) − 1 = ( 337 + 6 ) 2 − ( 337 ) 3 − ( 6 ) 3 337 − 6 = 337 + 2 337 ⋅ 6 + 6 − ( 337 − 6 ) ( 337 + 337 ⋅ 6 + 6 ) 337 − 6 = 343 + 2 2022 − ( 343 + 2022 ) = 2022 . \begin{aligned} &\frac{1}{\left(337^{\frac12}+6^{\frac12}\right)^{-2}} -\left(\frac{\sqrt{337}-\sqrt6}{337^{\frac32}-6^{\frac32}}\right)^{-1}\\ &=(\sqrt{337}+\sqrt6)^2-\frac{(\sqrt{337})^3-(\sqrt6)^3}{\sqrt{337}-\sqrt6}\\ &=337+2\sqrt{337\cdot6}+6 -\frac{(\sqrt{337}-\sqrt6)(337+\sqrt{337\cdot6}+6)}{\sqrt{337}-\sqrt6}\\ &=343+2\sqrt{2022}-(343+\sqrt{2022})=\sqrt{2022}. \end{aligned} ( 33 7 2 1 + 6 2 1 ) − 2 1 − ( 33 7 2 3 − 6 2 3 337 − 6 ) − 1 = ( 337 + 6 ) 2 − 337 − 6 ( 337 ) 3 − ( 6 ) 3 = 337 + 2 337 ⋅ 6 + 6 − 337 − 6 ( 337 − 6 ) ( 337 + 337 ⋅ 6 + 6 ) = 343 + 2 2022 − ( 343 + 2022 ) = 2022 . 