Solve y=-1/x-2+2

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

Solve for x

$$x=-\frac{5-2y}{y-2}$$

$$y\neq 2$$

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.

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

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

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

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

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

Subtract 4 from -1 to get -5.

$$yx-2y=-5+2x$$

Subtract 2x from both sides.

$$yx-2y-2x=-5$$

Add 2y to both sides.

$$yx-2x=-5+2y$$

Combine all terms containing x.

$$\left(y-2\right)x=-5+2y$$

The equation is in standard form.

$$\left(y-2\right)x=2y-5$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{2y-5}{y-2}$$

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

$$x=\frac{2y-5}{y-2}$$

Variable x cannot be equal to 2.

$$x=\frac{2y-5}{y-2}\text{, }x\neq 2$$

Solve for y

$$y=-\frac{5-2x}{x-2}$$

$$x\neq 2$$