Solve y=2-x/x+4

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

Solve for x

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

$$y\neq -1$$

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.

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

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

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

Add x to both sides.

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

Subtract 4y from both sides.

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

Combine all terms containing x.

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

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{2-4y}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

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

Divide 2-4y by y+1.

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

Variable x cannot be equal to -4.

$$x=\frac{2\left(1-2y\right)}{y+1}\text{, }x\neq -4$$

Solve for y

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

$$x\neq -4$$