Solve m-y=my+1

$$m - y = m y + 1$$

Solve for m

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

$$y\neq 1$$

Steps for Solving Linear Equation

Subtract my from both sides.

$$m-y-my=1$$

Add y to both sides.

$$m-my=1+y$$

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by -y+1.

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

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

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

Solve for y

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

$$m\neq -1$$

Steps for Solving Linear Equation

Subtract my from both sides.

$$m-y-my=1$$

Subtract m from both sides.

$$-y-my=1-m$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -1-m.

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

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

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

Divide 1-m by -1-m.

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