Solve 2x=y+1/y-2

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y-2.

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

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

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

Combine all terms containing x.

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

Divide both sides by 2y-4.

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

Dividing by 2y-4 undoes the multiplication by 2y-4.

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

Divide y+1 by 2y-4.

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

Solve for y

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

$$x\neq \frac{1}{2}$$

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.

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

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

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

Subtract y from both sides.

$$2xy-4x-y=1$$

Add 4x to both sides.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 2x-1.

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

Dividing by 2x-1 undoes the multiplication by 2x-1.

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

Variable y cannot be equal to 2.

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