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

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

Solve for x

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

$$y\neq 2$$

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

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

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

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

Add -2 and 2 to get 0.

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

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

$$2x=xy-y$$

Subtract xy from both sides.

$$2x-xy=-y$$

Combine all terms containing x.

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

Divide both sides by 2-y.

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

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

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of x-1,2.

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

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

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

Add -2 and 2 to get 0.

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

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

$$2x=xy-y$$

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

$$xy-y=2x$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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