Solve y=x+2/x-4

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

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.

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

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

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

Subtract x from both sides.

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

Add 4y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-1.

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

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

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

Divide 2+4y by y-1.

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

Variable x cannot be equal to 4.

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

Solve for y

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

$$x\neq 4$$