Solve 1-uy=u

$$1 - u y = u$$

Solve for u

$$u=\frac{1}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Subtract u from both sides.

$$1-uy-u=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-uy-u=-1$$

Combine all terms containing u.

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

Divide both sides by -y-1.

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

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

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

Divide -1 by -y-1.

$$u=\frac{1}{y+1}$$

Solve for y

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

$$u\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$-uy=u-1$$

The equation is in standard form.

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

Divide both sides by -u.

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

Dividing by -u undoes the multiplication by -u.

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

Divide u-1 by -u.

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