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\frac{\left(x-1\right)\left(x^{2}+x+1\right)\left(x^{6}+x^{3}+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
Factor the expressions that are not already factored.
x^{6}+x^{3}+1
Cancel out \left(x-1\right)\left(x^{2}+x+1\right) in both numerator and denominator.
\frac{\left(x-1\right)\left(x^{2}+x+1\right)\left(x^{6}+x^{3}+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
Factor the expressions that are not already factored.
x^{6}+x^{3}+1
Cancel out \left(x-1\right)\left(x^{2}+x+1\right) in both numerator and denominator.