Solve y=1-x/x-3

$$y= \frac{ 1-x }{ x-3 }$$

Solve for x

$$x=\frac{3y+1}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=1-x$$

Use the distributive property to multiply y by x-3.

$$yx-3y=1-x$$

Add x to both sides.

$$yx-3y+x=1$$

Add 3y to both sides.

$$yx+x=1+3y$$

Combine all terms containing x.

$$\left(y+1\right)x=1+3y$$

The equation is in standard form.

$$\left(y+1\right)x=3y+1$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{3y+1}{y+1}$$

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

$$x=\frac{3y+1}{y+1}$$

Variable x cannot be equal to 3.

$$x=\frac{3y+1}{y+1}\text{, }x\neq 3$$

Solve for y

$$y=-\frac{x-1}{x-3}$$

$$x\neq 3$$