Solve y=2x-1/2x+1

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

Solve for x

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

$$y\neq 1$$

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.

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

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

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

Subtract 2x from both sides.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2y-2.

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

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

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

Divide -1-y by 2y-2.

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

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

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

Solve for y

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

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