Сократите дробь: (x^4+2x^6+x^7)/(2+x+x^(-2)).

Ответ:

\[\frac{x^{4} + 2x^{6} + x^{7}}{2 + x + x^{- 2}} =\]

\[= \frac{x^{4}\left( 1 + 2x^{2} + x^{3} \right)}{2 + x + \frac{1}{x^{2}}} =\]

\[= \frac{x^{4}\left( 1 + 2x^{2} + x^{3} \right)}{\frac{2x^{2} + x^{3} + 1}{x^{2}}} =\]

\[= \frac{x^{4}\left( 1 + 2x^{2} + x^{3} \right) \cdot x²}{2x² + x³ + 1} = x^{6}\]