\(\frac{x^{10}-x^8-x^7+x^6+x^6+x^4-x^3-x^2+1}{x^{30}+x^{24}+x^{18}+x^{12}+x^6+1}=\frac{(x^{10}-x^8+x^6)-(x^7-x^5+x^3)+(x^4-x^2+1)}{ (x^{30}+x^{18}+x^{24})+(x^{12}+x^6+1)} \)

=\(\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+x^6+1)(x^{18}+1 )}=\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+2x^6+1-x^6) (x^6+1)(x^{12}-x^6+1)}=\frac{(x^4-x^2+1)(x^6-x^3+1)}{ (x^6-x^3+1)(x^6+x^3+1)(x^2+1)(x^4-x^2+1)(x^12-x^6+1 )} \)

=\(\frac{1}{(x^6+x^2+1)(x^2+1)(x^{12}-x^6+1)}\)

Tham khảo:

Mk làm luôn nhé , không chép lại đề đâu

Q = \(\dfrac{x^6\left(x^4-x^2+1\right)-x^3\left(x^4-x^2+1\right)+x^4-x^2+1}{x^{18}\left(x^{12}+x^6+1\right)+x^{12}+x^6+1}\)

\(Q=\dfrac{\left(x^4-x^2+1\right)\left(x^6-x^3+1\right)}{\left(x^{12}+x^6+1\right)\left(x^{18}+1\right)}\)

\(Q=\dfrac{\left(x^4-x^2+1\right)\left(x^6-x^3+1\right)}{\left(x^{12}+x^6+1\right)\left[\left(x^6\right)^3+1\right]}\)

\(Q=\dfrac{\left(x^4-x^2+1\right)\left(x^6-x^3+1\right)}{\left(x^{12}+2x^6+1-x^6\right)\left[\left(x^2\right)^3+1\right]\left(x^{12}-x^6+1\right)}\)

\(Q=\dfrac{\left(x^4-x^2+1\right)\left(x^6-x^3+1\right)}{\left[\left(x^6+1\right)-\left(x^3\right)^2\right]\left(x^2+1\right)\left(x^4-x^2+1\right)\left(x^{12}-x^6+1\right)}\)

\(Q=\dfrac{\left(x^6-x^3+1\right)}{\left(x^6-x^3+1\right)\left(x^6+1+x^3\right)\left(x^2+1\right)\left(x^{12}-x^6+1\right)}\)

\(Q=\dfrac{1}{\left(x^6+1+x^3\right)\left(x^2+1\right)\left(x^{12}-x^6+1\right)}\)

\(\frac{x^{24}+x^{18}+x^{12}+x^6+1}{x^{27}+x^{24}+x^{21}+x^{18}+x^{15}+x^{12}+x^9+x^6+x^3+1}=\frac{x^{24}+x^{18}+x^{12}+x^6+1}{x^{24}\left(x^3+1\right)+x^{18}\left(x^3+1\right)+x^{12}\left(x^3+1\right)+x^6\left(x^3+1\right)+\left(x^3+1\right)}\)

=\(\frac{x^{24}+x^{18}+x^{12}+x^6+1}{\left(x^3+1\right)\left(x^{24}+x^{18}+x^{12}+x^6+1\right)}=\frac{1}{x^3+1}\)