Solve y_{n}=2n-1/2n+1

$$y _ { n } = \frac { 2 n - 1 } { 2 n + 1 }$$

Solve for n

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

$$y_{n}\neq 1$$

Steps for Solving Linear Equation

Variable n cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2n+1.

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

Use the distributive property to multiply y_{n} by 2n+1.

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

Subtract 2n from both sides.

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

Subtract y_{n} from both sides.

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

Combine all terms containing n.

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

The equation is in standard form.

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

Divide both sides by 2y_{n}-2.

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

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

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

Divide -1-y_{n} by 2y_{n}-2.

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

Variable n cannot be equal to -\frac{1}{2}.

$$n=-\frac{y_{n}+1}{2\left(y_{n}-1\right)}\text{, }n\neq -\frac{1}{2}$$

Solve for y_n

$$y_{n}=-\frac{1-2n}{2n+1}$$

$$n\neq -\frac{1}{2}$$