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

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

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+2.

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

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

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

Use the distributive property to multiply y+2 by 3.

$$yx+2x+3y+6=y-2$$

Subtract 3y from both sides.

$$yx+2x+6=y-2-3y$$

Combine y and -3y to get -2y.

$$yx+2x+6=-2y-2$$

Subtract 6 from both sides.

$$yx+2x=-2y-2-6$$

Subtract 6 from -2 to get -8.

$$yx+2x=-2y-8$$

Combine all terms containing x.

$$\left(y+2\right)x=-2y-8$$

Divide both sides by y+2.

$$\frac{\left(y+2\right)x}{y+2}=\frac{-2y-8}{y+2}$$

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

$$x=\frac{-2y-8}{y+2}$$

Divide -2y-8 by y+2.

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

Solve for y

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

$$x\neq -2$$

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.

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

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

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

Use the distributive property to multiply y+2 by 3.

$$yx+2x+3y+6=y-2$$

Subtract y from both sides.

$$yx+2x+3y+6-y=-2$$

Combine 3y and -y to get 2y.

$$yx+2x+2y+6=-2$$

Subtract 2x from both sides.

$$yx+2y+6=-2-2x$$

Subtract 6 from both sides.

$$yx+2y=-2-2x-6$$

Subtract 6 from -2 to get -8.

$$yx+2y=-8-2x$$

Combine all terms containing y.

$$\left(x+2\right)y=-8-2x$$

The equation is in standard form.

$$\left(x+2\right)y=-2x-8$$

Divide both sides by 2+x.

$$\frac{\left(x+2\right)y}{x+2}=\frac{-2x-8}{x+2}$$

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

$$y=\frac{-2x-8}{x+2}$$

Divide -8-2x by 2+x.

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

Variable y cannot be equal to -2.

$$y=-\frac{2\left(x+4\right)}{x+2}\text{, }y\neq -2$$