Solve a_{n}=n/n+1

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

Solve for n

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

$$a_{n}\neq 1$$

Steps for Solving Linear Equation

Variable n cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by n+1.

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

Use the distributive property to multiply a_{n} by n+1.

$$a_{n}n+a_{n}=n$$

Subtract n from both sides.

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

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

$$a_{n}n-n=-a_{n}$$

Combine all terms containing n.

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

Divide both sides by a_{n}-1.

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

Dividing by a_{n}-1 undoes the multiplication by a_{n}-1.

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

Variable n cannot be equal to -1.

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

Solve for a_n

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

$$n\neq -1$$