How to find the dynamical equations of a two body problem ?

Question

Consider 2 stars with positions r1,r2 and masses m1, m2 which interact via their mutual gravitational attraction. What are the dynamical equations for $ \vec r_{1} $ and $ \vec r_{2} $ ? The answer in the solutions is $ m_{1}r''_{1} = -G_{N}m_{1}m_{2} \vec r_{1}-\vec r_{2}/|\vec r_{1} -r_{2}|^3 $ and similarly for m2. I can see that the equation has been derived using $ F=- \nabla V $ but I am really unsure of where the terms come from particularly the term in the denominator.