Solve a_{n}=2n+1/n+2

$$a _ { n } = \frac { 2 n + 1 } { n + 2 }$$

Solve for n

$$n=-\frac{2a_{n}-1}{a_{n}-2}$$

$$a_{n}\neq 2$$

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.

$$a_{n}\left(n+2\right)=2n+1$$

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

$$a_{n}n+2a_{n}=2n+1$$

Subtract 2n from both sides.

$$a_{n}n+2a_{n}-2n=1$$

Subtract 2a_{n} from both sides.

$$a_{n}n-2n=1-2a_{n}$$

Combine all terms containing n.

$$\left(a_{n}-2\right)n=1-2a_{n}$$

Divide both sides by a_{n}-2.

$$\frac{\left(a_{n}-2\right)n}{a_{n}-2}=\frac{1-2a_{n}}{a_{n}-2}$$

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

$$n=\frac{1-2a_{n}}{a_{n}-2}$$

Variable n cannot be equal to -2.

$$n=\frac{1-2a_{n}}{a_{n}-2}\text{, }n\neq -2$$

Solve for a_n

$$a_{n}=\frac{2n+1}{n+2}$$

$$n\neq -2$$