Solve 3-2x/x-1=y+1/x-1

$$\frac { 3 - 2 x } { x - 1 } = y + \frac { 1 } { x - 1 }$$

Solve for x

$$x\neq 1$$

$$y=-2\text{ and }x\neq 1$$

Steps for Solving Linear Equation

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

$$3-2x=\left(x-1\right)y+1$$

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

$$3-2x=xy-y+1$$

Subtract xy from both sides.

$$3-2x-xy=-y+1$$

Subtract 3 from both sides.

$$-2x-xy=-y+1-3$$

Subtract 3 from 1 to get -2.

$$-2x-xy=-y-2$$

Combine all terms containing x.

$$\left(-2-y\right)x=-y-2$$

The equation is in standard form.

$$\left(-y-2\right)x=-y-2$$

Divide both sides by -2-y.

$$\frac{\left(-y-2\right)x}{-y-2}=\frac{-y-2}{-y-2}$$

Dividing by -2-y undoes the multiplication by -2-y.

$$x=\frac{-y-2}{-y-2}$$

Divide -2-y by -2-y.

$$x=1$$

Variable x cannot be equal to 1.

$$x\in \emptyset$$

Solve for y

$$y=-2$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$3-2x=\left(x-1\right)y+1$$

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

$$3-2x=xy-y+1$$

Swap sides so that all variable terms are on the left hand side.

$$xy-y+1=3-2x$$

Subtract 1 from both sides.

$$xy-y=3-2x-1$$

Subtract 1 from 3 to get 2.

$$xy-y=2-2x$$

Combine all terms containing y.

$$\left(x-1\right)y=2-2x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)y}{x-1}=\frac{2-2x}{x-1}$$

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

$$y=\frac{2-2x}{x-1}$$

Divide 2-2x by x-1.

$$y=-2$$