Solve 2n-4/27n^2-54n+n-2/27n^2-54n

$$\frac { 2 n - 4 } { 27 n ^ { 2 } - 54 n } + \frac { n - 2 } { 27 n ^ { 2 } - 54 n }$$

Evaluate

$$\frac{1}{9n}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2n-4}{27n^{2}-54n}.

$$\frac{2\left(n-2\right)}{27n\left(n-2\right)}+\frac{n-2}{27n^{2}-54n}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{2}{27n}+\frac{n-2}{27n^{2}-54n}$$

Factor the expressions that are not already factored in \frac{n-2}{27n^{2}-54n}.

$$\frac{2}{27n}+\frac{n-2}{27n\left(n-2\right)}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{2}{27n}+\frac{1}{27n}$$

Since \frac{2}{27n} and \frac{1}{27n} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{27n}$$

Expand

$$\frac{1}{9n}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2n-4}{27n^{2}-54n}.

$$\frac{2\left(n-2\right)}{27n\left(n-2\right)}+\frac{n-2}{27n^{2}-54n}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{2}{27n}+\frac{n-2}{27n^{2}-54n}$$

Factor the expressions that are not already factored in \frac{n-2}{27n^{2}-54n}.

$$\frac{2}{27n}+\frac{n-2}{27n\left(n-2\right)}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{2}{27n}+\frac{1}{27n}$$

Since \frac{2}{27n} and \frac{1}{27n} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{27n}$$