Solve r+v=v*rTheta

$$r + v = v \cdot r \Theta$$

Solve for r

$$r=-\frac{v}{1-v\Theta }$$

$$\Theta =0\text{ or }v\neq \frac{1}{\Theta }$$

Steps for Solving Linear Equation

Subtract vr\Theta from both sides.

$$r+v-vr\Theta =0$$

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

$$r-vr\Theta =-v$$

Combine all terms containing r.

$$\left(1-v\Theta \right)r=-v$$

Divide both sides by 1-v\Theta .

$$\frac{\left(1-v\Theta \right)r}{1-v\Theta }=-\frac{v}{1-v\Theta }$$

Dividing by 1-v\Theta undoes the multiplication by 1-v\Theta .

$$r=-\frac{v}{1-v\Theta }$$

Solve for v

$$v=-\frac{r}{1-r\Theta }$$

$$\Theta =0\text{ or }r\neq \frac{1}{\Theta }$$

Steps for Solving Linear Equation

Subtract vr\Theta from both sides.

$$r+v-vr\Theta =0$$

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

$$v-vr\Theta =-r$$

Combine all terms containing v.

$$\left(1-r\Theta \right)v=-r$$

Divide both sides by 1-r\Theta .

$$\frac{\left(1-r\Theta \right)v}{1-r\Theta }=-\frac{r}{1-r\Theta }$$

Dividing by 1-r\Theta undoes the multiplication by 1-r\Theta .

$$v=-\frac{r}{1-r\Theta }$$