Solve 2n/n-2-1/3

$$\frac { 2 n } { n - 2 } - \frac { 1 } { 3 }$$

Evaluate

$$\frac{5n+2}{3\left(n-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n-2 and 3 is 3\left(n-2\right). Multiply \frac{2n}{n-2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{n-2}{n-2}.

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

Since \frac{3\times 2n}{3\left(n-2\right)} and \frac{n-2}{3\left(n-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2n-\left(n-2\right).

$$\frac{6n-n+2}{3\left(n-2\right)}$$

Combine like terms in 6n-n+2.

$$\frac{5n+2}{3\left(n-2\right)}$$

Expand 3\left(n-2\right).

$$\frac{5n+2}{3n-6}$$

Factor

$$\frac{5n+2}{3\left(n-2\right)}$$