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

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y-2.

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

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

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

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

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

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

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

Combine y and -y to get 0.

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

Add 2 and 2 to get 4.

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

Add y to both sides.

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

Subtract 2 from both sides.

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

Subtract 2 from 4 to get 2.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-2.

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

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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by y-2.

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

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

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

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

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

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

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

Combine y and -y to get 0.

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

Add 2 and 2 to get 4.

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

Add 2x to both sides.

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

Subtract 2 from both sides.

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

Subtract 2 from 4 to get 2.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

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

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

Divide 2+2x by x-1.

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

Variable y cannot be equal to 2.

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