Solve y-n=y+2/n

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

Solve for y

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

$$n\neq 1\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n.

$$ny-nn=y+2$$

Multiply n and n to get n^{2}.

$$ny-n^{2}=y+2$$

Subtract y from both sides.

$$ny-n^{2}-y=2$$

Add n^{2} to both sides.

$$ny-y=2+n^{2}$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by n-1.

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

Dividing by n-1 undoes the multiplication by n-1.

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

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=\frac{-\sqrt{y^{2}-4y-8}+y}{2}\text{, }&\text{unconditionally}\\n=\frac{\sqrt{y^{2}-4y-8}+y}{2}\text{, }&y\neq -2\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{y^{2}-4y-8}+y}{2}\text{, }&y\geq 2\sqrt{3}+2\text{ or }\left(y\neq -2\text{ and }y\leq 2-2\sqrt{3}\right)\\n=\frac{-\sqrt{y^{2}-4y-8}+y}{2}\text{, }&y\geq 2\sqrt{3}+2\text{ or }y\leq 2-2\sqrt{3}\end{matrix}\right.$$