Solve x/y-2+2/2-y=2quad

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

Solve for x

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

$$y\neq 2$$

Solution Steps

Multiply both sides of the equation by y-2, the least common multiple of y-2,2-y.

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

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

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

Add 2 to both sides.

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

Add -4 and 2 to get -2.

$$x=2y-2$$

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by y-2, the least common multiple of y-2,2-y.

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

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

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

Swap sides so that all variable terms are on the left hand side.

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

Add 4 to both sides.

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

Add -2 and 4 to get 2.

$$2y=x+2$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide x+2 by 2.

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

Variable y cannot be equal to 2.

$$y=\frac{x}{2}+1\text{, }y\neq 2$$