Synthesizable averaging scheme
The most direct solution would probably be to use a lookup table for \$\frac{1}{score1+score2}\$.

That would mean that you only need two adds and three multiplies.

If you need a result every clock, you'd have a three-stage pipeline:


In the first stage, compute


temp1 = score1 &times; value1
temp2 = score2 &times; value2
temp3 = score1 + score2

In the second stage, compute


temp4 = temp1 + temp2
temp5 = 1/temp3 (table lookup)

In the third stage, compute


result = temp4 &times; temp5