Giải thích các bước giải:
\(Q= \frac{x^{10}-x^{8}-x^{7}+x^{6}+x^{5}+x^{4}-x^{3}-x^{2}+1}{x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1}\)
Đặt \(A=x^{10}-x^{8}-x^{7}+x^{6}+x^{5}+x^{4}-x^{3}-x^{2}+1\)
\(A=(x^{10}+x^4)-(x^8+x^2)+(x^6+1)-x^7+x^5-x^3\)
\(=(x^6+1)(x^4-x^2+1)-x^3(x^4-x^2+1)\)
\(=(x^4-x^2+1)(x^6-x^3+1)\)
\(=\frac{(x^2+1)(x^4-x^2+1)(x^6-x^3+1)}{x^2+1}\)
\(=\frac{(x^6+1)(x^6-x^3+1)}{x^2+1}\)
Đặt \(B=x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1\)
\(= (x^6+1)(x^{24}+x^{12}+1)\)
Ta có:
\(Q=\frac{A}{B}=\frac{\frac{(x^6+1)(x^6-x^3+1)}{x^2+1}}{(x^6+1)(x^{24}+x^{12}+1)}=\frac{x^6-x^3+1}{(x^2+1)(x^{24}+x^{12}+1)}\)
