Answer
$F_{21} = -F_{12} = \frac{m_1}{m_1+m_2}F$
Work Step by Step
We start with the equation for acceleration, and then we simplify:
$a = \frac{F}{m} \\ a = \frac{F}{m_1+m_2} $
We know that $F_{12} = m_2a$, so it follows:
$F_{12} = \frac{m_2}{m_1+m_2}F$
Thus:
$F_{21} = -F_{12} = \frac{m_1}{m_1+m_2}F$
