Solve y=y/x-4

$$y= \frac{ y }{ x-4 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=0\text{, }&x\neq 4\\y\in \mathrm{C}\text{, }&x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{y}{x-4} from both sides.

$$y-\frac{y}{x-4}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{x-4}{x-4}.

$$\frac{y\left(x-4\right)}{x-4}-\frac{y}{x-4}=0$$

Since \frac{y\left(x-4\right)}{x-4} and \frac{y}{x-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\left(x-4\right)-y}{x-4}=0$$

Do the multiplications in y\left(x-4\right)-y.

$$\frac{yx-4y-y}{x-4}=0$$

Combine like terms in yx-4y-y.

$$\frac{yx-5y}{x-4}=0$$

Multiply both sides of the equation by x-4.

$$yx-5y=0$$

Combine all terms containing y.

$$\left(x-5\right)y=0$$

Divide 0 by x-5.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=5\text{, }&\text{unconditionally}\\x\neq 4\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.

$$y\left(x-4\right)=y$$

Use the distributive property to multiply y by x-4.

$$yx-4y=y$$

Add 4y to both sides.

$$yx=y+4y$$

Combine y and 4y to get 5y.

$$yx=5y$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{5y}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{5y}{y}$$

Divide 5y by y.

$$x=5$$

Solve for y

$$\left\{\begin{matrix}y=0\text{, }&x\neq 4\\y\in \mathrm{R}\text{, }&x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{y}{x-4} from both sides.

$$y-\frac{y}{x-4}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{x-4}{x-4}.

$$\frac{y\left(x-4\right)}{x-4}-\frac{y}{x-4}=0$$

Since \frac{y\left(x-4\right)}{x-4} and \frac{y}{x-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\left(x-4\right)-y}{x-4}=0$$

Do the multiplications in y\left(x-4\right)-y.

$$\frac{yx-4y-y}{x-4}=0$$

Combine like terms in yx-4y-y.

$$\frac{yx-5y}{x-4}=0$$

Multiply both sides of the equation by x-4.

$$yx-5y=0$$

Combine all terms containing y.

$$\left(x-5\right)y=0$$

Divide 0 by x-5.

$$y=0$$