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\frac{\frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}}}{\frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}}\times \frac{n}{3}
To raise \frac{n+2}{n-2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}\times \frac{n}{3}
Divide \frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}} by \frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12} by multiplying \frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}} by the reciprocal of \frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}.
\frac{3\left(n-2\right)^{2}\left(n+2\right)^{3}}{n\left(n+2\right)^{2}\left(n-2\right)^{3}}\times \frac{n}{3}
Factor the expressions that are not already factored in \frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}.
\frac{3\left(n+2\right)}{n\left(n-2\right)}\times \frac{n}{3}
Cancel out \left(n-2\right)^{2}\left(n+2\right)^{2} in both numerator and denominator.
\frac{3\left(n+2\right)n}{n\left(n-2\right)\times 3}
Multiply \frac{3\left(n+2\right)}{n\left(n-2\right)} times \frac{n}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{n+2}{n-2}
Cancel out 3n in both numerator and denominator.
\frac{\frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}}}{\frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}}\times \frac{n}{3}
To raise \frac{n+2}{n-2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}\times \frac{n}{3}
Divide \frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}} by \frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12} by multiplying \frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}} by the reciprocal of \frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}.
\frac{3\left(n-2\right)^{2}\left(n+2\right)^{3}}{n\left(n+2\right)^{2}\left(n-2\right)^{3}}\times \frac{n}{3}
Factor the expressions that are not already factored in \frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}.
\frac{3\left(n+2\right)}{n\left(n-2\right)}\times \frac{n}{3}
Cancel out \left(n-2\right)^{2}\left(n+2\right)^{2} in both numerator and denominator.
\frac{3\left(n+2\right)n}{n\left(n-2\right)\times 3}
Multiply \frac{3\left(n+2\right)}{n\left(n-2\right)} times \frac{n}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{n+2}{n-2}
Cancel out 3n in both numerator and denominator.