Solve y=2x+1/x+2

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

Solve for x

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

$$y\neq 2$$

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.

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

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

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

Subtract 2x from both sides.

$$yx+2y-2x=1$$

Subtract 2y from both sides.

$$yx-2x=1-2y$$

Combine all terms containing x.

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

Divide both sides by y-2.

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

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

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

Variable x cannot be equal to -2.

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

Solve for y

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

$$x\neq -2$$