$2\mathrm{.}15$ Prove the following using appropriate methods.

a$.\frac{?}{\text{b}\text{a}\text{r}}(AC)+AB\frac{+}{b}ar(BC)\frac{?}{b}=ar(AB)+BC+\frac{A}{b}ar(C)$

b$.\frac{A}{b}ar(C)+BC+\frac{A}{b}ar\frac{B}{b}ar(BC)\frac{+}{b}ar(AB)+AC$