Solve (x+1)y+(y-1)x=1

$$(x+1)y+(y-1)x=1$$

Solve for x

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

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

Steps for Solving Linear Equation

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

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

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

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

Combine xy and yx to get 2xy.

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

Subtract y from both sides.

$$2xy-x=1-y$$

Combine all terms containing x.

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

Divide both sides by 2y-1.

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

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

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

Solve for y

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

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

Steps for Solving Linear Equation

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

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

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

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

Combine xy and yx to get 2xy.

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

Add x to both sides.

$$2xy+y=1+x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 2x+1.

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

Dividing by 2x+1 undoes the multiplication by 2x+1.

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