Solve a_{n}=(5n+18/n+2)

$$a _ { n } = ( \frac { 5 n + 18 } { n + 2 } )$$

Solve for n

$$n=-\frac{2\left(a_{n}-9\right)}{a_{n}-5}$$

$$a_{n}\neq 5$$

Steps for Solving Linear Equation

Variable n cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by n+2.

$$a_{n}\left(n+2\right)=5n+18$$

Use the distributive property to multiply a_{n} by n+2.

$$a_{n}n+2a_{n}=5n+18$$

Subtract 5n from both sides.

$$a_{n}n+2a_{n}-5n=18$$

Subtract 2a_{n} from both sides.

$$a_{n}n-5n=18-2a_{n}$$

Combine all terms containing n.

$$\left(a_{n}-5\right)n=18-2a_{n}$$

Divide both sides by a_{n}-5.

$$\frac{\left(a_{n}-5\right)n}{a_{n}-5}=\frac{18-2a_{n}}{a_{n}-5}$$

Dividing by a_{n}-5 undoes the multiplication by a_{n}-5.

$$n=\frac{18-2a_{n}}{a_{n}-5}$$

Divide 18-2a_{n} by a_{n}-5.

$$n=\frac{2\left(9-a_{n}\right)}{a_{n}-5}$$

Variable n cannot be equal to -2.

$$n=\frac{2\left(9-a_{n}\right)}{a_{n}-5}\text{, }n\neq -2$$

Solve for a_n

$$a_{n}=\frac{5n+18}{n+2}$$

$$n\neq -2$$