Solve (n+2/n-2)^3/frac{n^3+4n^2+4n{3n^2-12n+12}}*n/3

$$\frac { ( \frac { n + 2 } { n - 2 } ) ^ { 3 } } { \frac { n ^ { 3 } + 4 n ^ { 2 } + 4 n } { 3 n ^ { 2 } - 12 n + 12 } } \cdot \frac { n } { 3 }$$

Evaluate

$$\frac{n+2}{n-2}$$

Short Solution Steps

To raise \frac{n+2}{n-2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}}}{\frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}}\times \frac{n}{3}$$

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}.

$$\frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}\times \frac{n}{3}$$

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)}.

$$\frac{3\left(n-2\right)^{2}\left(n+2\right)^{3}}{n\left(n+2\right)^{2}\left(n-2\right)^{3}}\times \frac{n}{3}$$

Cancel out \left(n-2\right)^{2}\left(n+2\right)^{2} in both numerator and denominator.

$$\frac{3\left(n+2\right)}{n\left(n-2\right)}\times \frac{n}{3}$$

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.

$$\frac{3\left(n+2\right)n}{n\left(n-2\right)\times 3}$$

Cancel out 3n in both numerator and denominator.

$$\frac{n+2}{n-2}$$

Expand

$$\frac{n+2}{n-2}$$

Short Solution Steps

To raise \frac{n+2}{n-2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(n+2\right)^{3}}{\left(n-2\right)^{3}}}{\frac{n^{3}+4n^{2}+4n}{3n^{2}-12n+12}}\times \frac{n}{3}$$

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}.

$$\frac{\left(n+2\right)^{3}\left(3n^{2}-12n+12\right)}{\left(n-2\right)^{3}\left(n^{3}+4n^{2}+4n\right)}\times \frac{n}{3}$$

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)}.

$$\frac{3\left(n-2\right)^{2}\left(n+2\right)^{3}}{n\left(n+2\right)^{2}\left(n-2\right)^{3}}\times \frac{n}{3}$$

Cancel out \left(n-2\right)^{2}\left(n+2\right)^{2} in both numerator and denominator.

$$\frac{3\left(n+2\right)}{n\left(n-2\right)}\times \frac{n}{3}$$

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.

$$\frac{3\left(n+2\right)n}{n\left(n-2\right)\times 3}$$

Cancel out 3n in both numerator and denominator.

$$\frac{n+2}{n-2}$$