Solve a_{n}=2n/n+6

$$a _ { n } = \frac { 2 n } { n + 6 }$$

Solve for n

$$n=\frac{6a_{n}}{2-a_{n}}$$

$$a_{n}\neq 2$$

Steps for Solving Linear Equation

Variable n cannot be equal to -6 since division by zero is not defined. Multiply both sides of the equation by n+6.

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

Use the distributive property to multiply a_{n} by n+6.

$$a_{n}n+6a_{n}=2n$$

Subtract 2n from both sides.

$$a_{n}n+6a_{n}-2n=0$$

Subtract 6a_{n} from both sides. Anything subtracted from zero gives its negation.

$$a_{n}n-2n=-6a_{n}$$

Combine all terms containing n.

$$\left(a_{n}-2\right)n=-6a_{n}$$

Divide both sides by a_{n}-2.

$$\frac{\left(a_{n}-2\right)n}{a_{n}-2}=-\frac{6a_{n}}{a_{n}-2}$$

Dividing by a_{n}-2 undoes the multiplication by a_{n}-2.

$$n=-\frac{6a_{n}}{a_{n}-2}$$

Variable n cannot be equal to -6.

$$n=-\frac{6a_{n}}{a_{n}-2}\text{, }n\neq -6$$

Solve for a_n

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

$$n\neq -6$$