Найдите значение выражения z8−z4z4(z+1)⋅15(z−1)(z2+1)\frac{z^8-z^4}{z^4(z+1)}\cdot \frac{15}{(z-1)(z^2+1)}z4(z+1)z8−z4⋅(z−1)(z2+1)15▸Ответ15▸Решениеz8−z4z4(z+1)⋅15(z−1)(z2+1)=\frac{z^8-z^4}{z^4(z+1)}\cdot \frac{15}{(z-1)(z^2+1)}=z4(z+1)z8−z4⋅(z−1)(z2+1)15=z4(z4−1)z4(z+1)⋅15(z−1)(z2+1)=\frac{z^4(z^4-1)}{z^4(z+1)}\cdot \frac{15}{(z-1)(z^2+1)}=z4(z+1)z4(z4−1)⋅(z−1)(z2+1)15=(z2+1)(z2−1)z+1⋅\frac{(z^2+1)(z^2-1)}{z+1}\cdotz+1(z2+1)(z2−1)⋅15(z−1)(z2+1)= \frac{15}{(z-1)(z^2+1)}=(z−1)(z2+1)15=(z+1)(z−1)z+1⋅15z−1=15\frac{(z+1)(z-1)}{z+1}\cdot \frac{15}{z-1}=15z+1(z+1)(z−1)⋅z−115=15