Solve y=-2-3/x-2

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

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Subtract 3 from 4 to get 1.

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

Add 2x to both sides.

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

Add 2y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y+2.

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

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

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

Variable x cannot be equal to 2.

$$x=\frac{2y+1}{y+2}\text{, }x\neq 2$$

Solve for y

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

$$x\neq 2$$