Сократите дробь: (a^7-a^4)/(a^6-1).

Ответ:

\[\frac{a^{7} - a^{4}}{a^{6} - 1} = \frac{a^{4}\left( a^{3} - 1 \right)}{\left( a^{2} \right)^{3} - 1^{3}} =\]

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

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

\[или\]

\[\frac{a^{7} - a^{4}}{a^{6} - 1} = \frac{a^{4}\left( a^{3} - 1 \right)}{\left( a^{3} \right)^{2} - 1^{2}} =\]

\[= \frac{a^{4}(a^{3} - 1)}{(a^{3} - 1)(a^{3} + 1)} = \frac{a^{4}}{a^{3} + 1}\]