Solve y=x/2x-1

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

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-1.

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

Use the distributive property to multiply y by 2x-1.

$$2yx-y=x$$

Subtract x from both sides.

$$2yx-y-x=0$$

Add y to both sides. Anything plus zero gives itself.

$$2yx-x=y$$

Combine all terms containing x.

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

Divide both sides by 2y-1.

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

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

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

Variable x cannot be equal to \frac{1}{2}.

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

Solve for y

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

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