Solve y+y(x)-x=0

$$y + y ( x ) - x = 0$$

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

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

$$yx-x=-y$$

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.

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

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Add x to both sides. Anything plus zero gives itself.

$$y+yx=x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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