Solve y=y/x-1

$$y = \frac { y } { x } - 1$$

Solve for x

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

$$y\neq 0\text{ and }y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$yx=y+x\left(-1\right)$$

Subtract x\left(-1\right) from both sides.

$$yx-x\left(-1\right)=y$$

Multiply -1 and -1 to get 1.

$$yx+x=y$$

Combine all terms containing x.

$$\left(y+1\right)x=y$$

Divide both sides by y+1.

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

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

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

Variable x cannot be equal to 0.

$$x=\frac{y}{y+1}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{x}{x-1}$$

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

Since \frac{y}{x} and \frac{x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

Since \frac{yx}{x} and \frac{y-x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Multiply both sides of the equation by x.

$$yx-y+x=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$yx-y=-x$$

Combine all terms containing y.

$$\left(x-1\right)y=-x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)y}{x-1}=-\frac{x}{x-1}$$

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

$$y=-\frac{x}{x-1}$$