Solve 2x-1/x-1=y

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

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

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

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

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

Subtract yx from both sides.

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

Add 1 to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y+2.

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

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

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

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

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

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

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

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

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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