$$\frac{ 1+ { x }^{ 11 } }{ 1+x }$$
$\frac{x^{11}+1}{x+1}$
$$\frac{\left(x+1\right)\left(x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1\right)}{x+1}$$
$$x^{10}-x^{9}+x^{8}-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+1$$
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