Solve x=-1/y-1+3

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

Solve for y

$$y=-\frac{4-x}{x-3}$$

$$x\neq 3$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by y-1.

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

Use the distributive property to multiply x by y-1.

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

Use the distributive property to multiply y-1 by 3.

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

Subtract 3 from -1 to get -4.

$$xy-x=-4+3y$$

Subtract 3y from both sides.

$$xy-x-3y=-4$$

Add x to both sides.

$$xy-3y=-4+x$$

Combine all terms containing y.

$$\left(x-3\right)y=-4+x$$

The equation is in standard form.

$$\left(x-3\right)y=x-4$$

Divide both sides by x-3.

$$\frac{\left(x-3\right)y}{x-3}=\frac{x-4}{x-3}$$

Dividing by x-3 undoes the multiplication by x-3.

$$y=\frac{x-4}{x-3}$$

Variable y cannot be equal to 1.

$$y=\frac{x-4}{x-3}\text{, }y\neq 1$$

Solve for x

$$x=-\frac{4-3y}{y-1}$$

$$y\neq 1$$