Найдите значение дроби: (a^6+1)/(a^10+a^4) при a=0,1; a=-1/2.

Ответ:

\[\frac{a^{6} + 1}{a^{10} + a^{4}} = \frac{a^{6} + 1}{a^{4}(a^{6} + 1)} = \frac{1}{a^{4}}\]

\[a = 0,1:\]

\[\frac{1}{a^{4}} = \frac{1}{(0,1)^{4}} = \frac{1}{0,0001} = 10\ 000.\]

\[a = - \frac{1}{2}:\]

\[\frac{1}{a^{4}} = \frac{1}{\left( - \frac{1}{2} \right)^{4}} = \frac{1}{\frac{1}{16}} = 16.\]