Trying to understand this summation property $\sum_{i} \frac{a_i(b_i + rc_i)}{1+rd_i}$

Question

I'm having a big problem trying to understand how to go from this

$$\sum_{i} \frac{a_i(b_i + rc_i)}{1+rd_i} $$

to this

$$\sum_{k} a_k(b_k+rc_k)\prod_{j\neq k}(1+rd_j) $$

The idea is that the summation in the first equation needs to be rewritten in the summation/product form in the second equation in order to later expand the product term.

Any tips, clues or comments are much appreciated.

Thanks