Solve 2x+3/x+2=y

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

Solve for x

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

$$y\neq 2$$

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.

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

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

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

Subtract yx from both sides.

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

Subtract 3 from both sides.

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

Combine all terms containing x.

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

Divide both sides by -y+2.

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

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

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

Variable x cannot be equal to -2.

$$x=\frac{2y-3}{2-y}\text{, }x\neq -2$$

Solve for y

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

$$x\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+2.

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

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

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

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

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

Combine all terms containing y.

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

Divide both sides by x+2.

$$\frac{\left(x+2\right)y}{x+2}=\frac{2x+3}{x+2}$$

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

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