$Q=\frac{(x^{10}-x^8+x^6)-(x^7-x^5+x^3)+(x^4-x^2+1)}{x^{18}(x^{12}+x^6+1)+x^{12}+x^6+1}$
$=\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+x^6+1)(x^{18}+1)}$
$=\frac{(x^4-x^2+1)(x^6-x^3+1)}{(x^{12}+2x^6+1-x^6)(x^6+1)(x^{12}-x^6+1)}$
$=\frac{(x^4-x^2+1)(x^6-x^3+1)}{[(x^6+1)^2-x^6](x^2+1)(x^4-x^2+1)(x^{12}-x^6+1)}$
$=\frac{x^6-x^3+1}{(x^6+x^3+1)(x^6-x^3+1)(x^2+1)(x^{12}-x^6+1)}$
$=\frac{1}{(x^6+x^3+1)(x^2+1)(x^{12}-x^6+1)}$