Solve y=2+1/x+3

$$y = 2 + \frac { 1 } { x + 3 }$$

Solve for x

$$x=-\frac{7-3y}{2-y}$$

$$y\neq 2$$

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.

$$y\left(x+3\right)=\left(x+3\right)\times 2+1$$

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

$$yx+3y=\left(x+3\right)\times 2+1$$

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

$$yx+3y=2x+6+1$$

Add 6 and 1 to get 7.

$$yx+3y=2x+7$$

Subtract 2x from both sides.

$$yx+3y-2x=7$$

Subtract 3y from both sides.

$$yx-2x=7-3y$$

Combine all terms containing x.

$$\left(y-2\right)x=7-3y$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{7-3y}{y-2}$$

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

$$x=\frac{7-3y}{y-2}$$

Variable x cannot be equal to -3.

$$x=\frac{7-3y}{y-2}\text{, }x\neq -3$$

Solve for y

$$y=\frac{2x+7}{x+3}$$

$$x\neq -3$$