= Solution
In the intended comparison of emission and reception epochs, with negligible <peculiar velocities>, the Earth-observed <cosmological redshifts> correspond to $a_A=a_0/2$ and $a_B=a_0/10$. A photon emitted at the B epoch and received at the A epoch consequently has
$$
\boxed{1+z_{B\to A}=\frac{a_A}{a_B}=\frac{10}{2}=5,
\qquad z_{B\to A}=4.}
$$
These factors divide, whereas the redshifts themselves do not subtract. There is a geometrical qualification to this usual answer: the two Earth-observed redshifts alone do not specify an arbitrary actual B-to-A observation. The assumed events must be connected by a <null geodesic>, as when A is on the same radial photon path between B and Earth. If the galaxies have an unspecified angular separation, or A observes at a different <cosmic time>, the B emission event reaching A is different and its redshift is not determined by these two numbers alone.
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