Solve y=1/x+4+2

$$y = \frac { 1 } { x + 4 } + 2$$

Solve for x

$$x=-\frac{9-4y}{2-y}$$

$$y\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.

$$y\left(x+4\right)=1+\left(x+4\right)\times 2$$

Use the distributive property to multiply y by x+4.

$$yx+4y=1+\left(x+4\right)\times 2$$

Use the distributive property to multiply x+4 by 2.

$$yx+4y=1+2x+8$$

Add 1 and 8 to get 9.

$$yx+4y=9+2x$$

Subtract 2x from both sides.

$$yx+4y-2x=9$$

Subtract 4y from both sides.

$$yx-2x=9-4y$$

Combine all terms containing x.

$$\left(y-2\right)x=9-4y$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{9-4y}{y-2}$$

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

$$x=\frac{9-4y}{y-2}$$

Variable x cannot be equal to -4.

$$x=\frac{9-4y}{y-2}\text{, }x\neq -4$$

Solve for y

$$y=\frac{2x+9}{x+4}$$

$$x\neq -4$$