Solve y=2x+9/x+3

$$y = \frac { 2 x + 9 } { x + 3 }$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

$$y\left(x+3\right)=2x+9$$

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

$$yx+3y=2x+9$$

Subtract 2x from both sides.

$$yx+3y-2x=9$$

Subtract 3y from both sides.

$$yx-2x=9-3y$$

Combine all terms containing x.

$$\left(y-2\right)x=9-3y$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{9-3y}{y-2}$$

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

$$x=\frac{9-3y}{y-2}$$

Divide 9-3y by y-2.

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

Variable x cannot be equal to -3.

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

Solve for y

$$y=\frac{2x+9}{x+3}$$

$$x\neq -3$$