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

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

Solve for x

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

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

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 2\left(x-1\right), the least common multiple of 2,x-1.

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

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

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

Multiply -1 and 2 to get -2.

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

Multiply 2 and \frac{1}{2} to get 1.

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

Add -1 and 2 to get 1.

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

Subtract x from both sides.

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

Add 2y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2y-1.

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

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

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1$$