Solve 24+6n/6+n-4/n

$$\frac { \frac { 24 + 6 n } { 6 + n } - 4 } { n }$$

Evaluate

$$\frac{2}{n+6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{6+n}{6+n}.

$$\frac{\frac{24+6n}{6+n}-\frac{4\left(6+n\right)}{6+n}}{n}$$

Since \frac{24+6n}{6+n} and \frac{4\left(6+n\right)}{6+n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{24+6n-4\left(6+n\right)}{6+n}}{n}$$

Do the multiplications in 24+6n-4\left(6+n\right).

$$\frac{\frac{24+6n-24-4n}{6+n}}{n}$$

Combine like terms in 24+6n-24-4n.

$$\frac{\frac{2n}{6+n}}{n}$$

Express \frac{\frac{2n}{6+n}}{n} as a single fraction.

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

Cancel out n in both numerator and denominator.

$$\frac{2}{n+6}$$

Expand

$$\frac{2}{n+6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{6+n}{6+n}.

$$\frac{\frac{24+6n}{6+n}-\frac{4\left(6+n\right)}{6+n}}{n}$$

Since \frac{24+6n}{6+n} and \frac{4\left(6+n\right)}{6+n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{24+6n-4\left(6+n\right)}{6+n}}{n}$$

Do the multiplications in 24+6n-4\left(6+n\right).

$$\frac{\frac{24+6n-24-4n}{6+n}}{n}$$

Combine like terms in 24+6n-24-4n.

$$\frac{\frac{2n}{6+n}}{n}$$

Express \frac{\frac{2n}{6+n}}{n} as a single fraction.

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

Cancel out n in both numerator and denominator.

$$\frac{2}{n+6}$$