Question

Сократите:  64a^12-b^9/ 64a^12-48a^8b^3+12a^4b^6-b^9
Пожалуйста.....)))))))) Помогите:))))))))

Answer 1

$frac {64a^{12}-b^9}{64a^{12}-48a^8b^3+12a^4b^6-b^9}=\ frac {(4a^4-b^3)(16a^8+4a^4b^3+b^6)}{(64a^{12}-b^9)-(48a^8b^3-12a^4b^6)}=\ frac {(4a^4-b^3)(16a^8+4a^4b^3+b^6)}{(4a^4-b^3)(16a^8+4a^4b^3+b^6)-12a^4b^3(4a^4-b^3)}=\ frac {(4a^4-b^3)(16a^8+4a^4b^3+b^6)}{(4a^4-b^3)(16a^8+4a^4b^3+b^6-12a^4b^3)}=\ frac {16a^8+4a^4b^3+b^6}{16a^8+4a^4b^3+b^6-12a^4b^3}=\ frac {16a^8+4a^4b^3+b^6}{16a^8-8a^4b^3+b^6}=\ frac {16a^8+4a^4b^3+b^6}{(4a^4-b^3)^2}$