Solve y=-x-2/x+2

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

Solve for x

$$x\neq -2$$

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

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.

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

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

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

Add x to both sides.

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

Subtract 2y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y+1.

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

Dividing by y+1 undoes the multiplication by y+1.

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

Divide -2-2y by y+1.

$$x=-2$$

Variable x cannot be equal to -2.

$$x\in \emptyset$$

Solve for y

$$y=-1$$

$$x\neq -2$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{-x-2}{x+2}.

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

Extract the negative sign in -x-2.

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

Cancel out x+2 in both numerator and denominator.

$$y=-1$$