@abcdw Look, Claude 3.5 has found a solution!

a = b = c = 4

4/(4+4) + 4/(4+4) + 4/(4+4)
= 4/8 + 4/8 + 4/8
= 1/2 + 1/2 + 1/2
= 3/2 + 1/2
= 4