How to factor $ {s – a_m} over {s-b_n} $ to $ {1-{s over a_m}} over {1 – {s over b_n}} $

I saw this polynomial or algebraic equation and can verified by plugging in some numbers and figuring out the constant for a specific sets of $ a_m $ and $ b_n $. But how can I derive the equation on the right from the left? I tried multiplying both sides by s, a or b but I can’t come up with anything close to the term on the right.

${{(s-a_1)(s – a_2) ; … ; (s-a_m)} over {(s-b_1)(s-b_2) ; … ; (s-b_n)}} = C_0 {({1-{s over a_1})({1 – {s over a_2}}) ; … ;({1 – {s over a_m}})} over {({1 – {s over b_1}})({1 – {s over b_2}}) ; … ; ({1 – {s over b_n}})}}$