Solve -x*y+u=y-u/x

$$- x \times y + u = y - \frac { u } { x }$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=xy\text{, }&x\neq 0\\u\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$\left(-x\right)yx+xu=xy-u$$

Add u to both sides.

$$\left(-x\right)yx+xu+u=xy$$

Subtract \left(-x\right)yx from both sides.

$$xu+u=xy-\left(-x\right)yx$$

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

$$xu+u=xy-\left(-x^{2}y\right)$$

Multiply -1 and -1 to get 1.

$$xu+u=xy+x^{2}y$$

Combine all terms containing u.

$$\left(x+1\right)u=xy+x^{2}y$$

The equation is in standard form.

$$\left(x+1\right)u=xy+yx^{2}$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)u}{x+1}=\frac{xy\left(x+1\right)}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$u=\frac{xy\left(x+1\right)}{x+1}$$

Divide xy\left(1+x\right) by x+1.

$$u=xy$$

Solve for u

$$\left\{\begin{matrix}u=xy\text{, }&x\neq 0\\u\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$\left(-x\right)yx+xu=xy-u$$

Add u to both sides.

$$\left(-x\right)yx+xu+u=xy$$

Subtract \left(-x\right)yx from both sides.

$$xu+u=xy-\left(-x\right)yx$$

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

$$xu+u=xy-\left(-x^{2}y\right)$$

Multiply -1 and -1 to get 1.

$$xu+u=xy+x^{2}y$$

Combine all terms containing u.

$$\left(x+1\right)u=xy+x^{2}y$$

The equation is in standard form.

$$\left(x+1\right)u=xy+yx^{2}$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)u}{x+1}=\frac{xy\left(x+1\right)}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$u=\frac{xy\left(x+1\right)}{x+1}$$

Divide xy\left(1+x\right) by x+1.

$$u=xy$$

Solve for x

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