Solve p+q=q/p+2

$$p + q = \frac { q } { p } + 2$$

Solve for q

$$q=-\frac{p\left(p-2\right)}{p-1}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by p.

$$pp+pq=q+p\times 2$$

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

$$p^{2}+pq=q+p\times 2$$

Subtract q from both sides.

$$p^{2}+pq-q=p\times 2$$

Subtract p^{2} from both sides.

$$pq-q=p\times 2-p^{2}$$

Combine all terms containing q.

$$\left(p-1\right)q=p\times 2-p^{2}$$

The equation is in standard form.

$$\left(p-1\right)q=2p-p^{2}$$

Divide both sides by p-1.

$$\frac{\left(p-1\right)q}{p-1}=\frac{p\left(2-p\right)}{p-1}$$

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

$$q=\frac{p\left(2-p\right)}{p-1}$$

Solve for p

$$\left\{\begin{matrix}\\p=\frac{\sqrt{q^{2}+4}}{2}-\frac{q}{2}+1\text{, }&\text{unconditionally}\\p=-\frac{\sqrt{q^{2}+4}}{2}-\frac{q}{2}+1\text{, }&q\neq 0\end{matrix}\right.$$