Another approach to velocity transformations in Figure reference frames B and C move past reference frame A

Question:

Another approach to velocity transformations in Figure reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocity of one frame relative to another with a two-letter subscript. For example, v AB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, β AB (=, v AB/c) is the speed parameter corresponding to v AB.

(a) Show that β AC = β AB + β BC / 1 + β AB β BC, Let MAB represent the ratio (1 = β AB) (1 + β AB), and let MBC and MAC represent similar ratios.

(b) Show that the relation MAC = MABMBC is true by deriving the equation of part (a) from it.