Solve (1-x)y=x+1

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

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

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

$$y-xy=x+1$$

Subtract x from both sides.

$$y-xy-x=1$$

Subtract y from both sides.

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

Combine all terms containing x.

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

Divide both sides by -y-1.

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

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

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

Divide 1-y by -y-1.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$y-xy=x+1$$

Combine all terms containing y.

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

Divide both sides by 1-x.

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

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

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