Solve y=1/x+4-2

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

Solve for x

$$x=-\frac{4y+7}{y+2}$$

$$y\neq -2$$

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.

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

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

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

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

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

Subtract 8 from 1 to get -7.

$$yx+4y=-7-2x$$

Add 2x to both sides.

$$yx+4y+2x=-7$$

Subtract 4y from both sides.

$$yx+2x=-7-4y$$

Combine all terms containing x.

$$\left(y+2\right)x=-7-4y$$

The equation is in standard form.

$$\left(y+2\right)x=-4y-7$$

Divide both sides by y+2.

$$\frac{\left(y+2\right)x}{y+2}=\frac{-4y-7}{y+2}$$

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

$$x=\frac{-4y-7}{y+2}$$

Divide -7-4y by y+2.

$$x=-\frac{4y+7}{y+2}$$

Variable x cannot be equal to -4.

$$x=-\frac{4y+7}{y+2}\text{, }x\neq -4$$

Solve for y

$$y=-\frac{2x+7}{x+4}$$

$$x\neq -4$$