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\frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)a^{2}\left(a+1\right)^{2}}
Factor the expressions that are not already factored.
\frac{a^{2}+a+1}{a^{2}\left(a+1\right)^{2}}
Cancel out a-1 in both numerator and denominator.
\frac{a^{2}+a+1}{a^{4}+2a^{3}+a^{2}}
Expand the expression.
\frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)a^{2}\left(a+1\right)^{2}}
Factor the expressions that are not already factored.
\frac{a^{2}+a+1}{a^{2}\left(a+1\right)^{2}}
Cancel out a-1 in both numerator and denominator.
\frac{a^{2}+a+1}{a^{4}+2a^{3}+a^{2}}
Expand the expression.