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

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

Solve for x

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

$$y\neq 2$$

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.

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

Use the distributive property to multiply 2y by x-1.

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

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

$$x+2=2yx-2y-3x+3$$

Subtract 2yx from both sides.

$$x+2-2yx=-2y-3x+3$$

Add 3x to both sides.

$$x+2-2yx+3x=-2y+3$$

Combine x and 3x to get 4x.

$$4x+2-2yx=-2y+3$$

Subtract 2 from both sides.

$$4x-2yx=-2y+3-2$$

Subtract 2 from 3 to get 1.

$$4x-2yx=-2y+1$$

Combine all terms containing x.

$$\left(4-2y\right)x=-2y+1$$

The equation is in standard form.

$$\left(4-2y\right)x=1-2y$$

Divide both sides by -2y+4.

$$\frac{\left(4-2y\right)x}{4-2y}=\frac{1-2y}{4-2y}$$

Dividing by -2y+4 undoes the multiplication by -2y+4.

$$x=\frac{1-2y}{4-2y}$$

Divide -2y+1 by -2y+4.

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

Variable x cannot be equal to 1.

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

Solve for y

$$y=-\frac{4x-1}{2\left(1-x\right)}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

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

Use the distributive property to multiply 2y by x-1.

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

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

$$x+2=2yx-2y-3x+3$$

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

$$2yx-2y-3x+3=x+2$$

Add 3x to both sides.

$$2yx-2y+3=x+2+3x$$

Combine x and 3x to get 4x.

$$2yx-2y+3=4x+2$$

Subtract 3 from both sides.

$$2yx-2y=4x+2-3$$

Subtract 3 from 2 to get -1.

$$2yx-2y=4x-1$$

Combine all terms containing y.

$$\left(2x-2\right)y=4x-1$$

Divide both sides by 2x-2.

$$\frac{\left(2x-2\right)y}{2x-2}=\frac{4x-1}{2x-2}$$

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

$$y=\frac{4x-1}{2x-2}$$

Divide 4x-1 by 2x-2.

$$y=\frac{4x-1}{2\left(x-1\right)}$$