Solve 1/xy=x+2

$$\frac { 1 } { x } y = x + 2$$

Solve for y

$$y=x\left(x+2\right)$$

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by x.

$$1y=xx+x\times 2$$

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

$$1y=x^{2}+x\times 2$$

Reorder the terms.

$$y=x^{2}+2x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\sqrt{y+1}-1\text{, }&\text{unconditionally}\\x=\sqrt{y+1}-1\text{, }&y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{y+1}-1\text{, }&y\neq 0\text{ and }y\geq -1\\x=-\sqrt{y+1}-1\text{, }&y\geq -1\end{matrix}\right.$$