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\frac{\frac{1}{3}\left(a-1\right)\left(3a^{2}+a+2\right)}{\frac{1}{3}\left(3a+1\right)}
Factor the expressions that are not already factored.
\frac{\left(a-1\right)\left(3a^{2}+a+2\right)}{\left(\frac{1}{3}\right)^{0}\left(3a+1\right)}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{3a^{3}-2a^{2}+a-2}{3a+1}
Expand the expression.
\frac{\frac{1}{3}\left(a-1\right)\left(3a^{2}+a+2\right)}{\frac{1}{3}\left(3a+1\right)}
Factor the expressions that are not already factored.
\frac{\left(a-1\right)\left(3a^{2}+a+2\right)}{\left(\frac{1}{3}\right)^{0}\left(3a+1\right)}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{3a^{3}-2a^{2}+a-2}{3a+1}
Expand the expression.