If V = 12R / (r + R), then R = ?

Concept: To rearrange a literal equation for a specified variable, clear any fraction by cross-multiplication, expand the brackets, collect every term containing the target variable on one side, factor that variable out, and divide by its remaining coefficient.

Application:

1. Start from the given relation V = 12R/(r + R).

2. Cross-multiply to clear the fraction: V(r + R) = 12R.

3. Expand the left side: Vr + VR = 12R.

4. Move every R-term to one side: Vr = 12R - VR.

5. Factor R out of the right side: Vr = R(12 - V).

6. Divide both sides by (12 - V) to isolate R: R = Vr/(12 - V).

Cross-check: substituting R = Vr/(12 - V) back gives r + R = 12r/(12 - V), so 12R/(r + R) simplifies to V again, confirming the original equation is satisfied.