why not

first son:

(1/2)/[(1/2)+(1/3)+(1/9)]=(9/17) its clear?its ok?

second son
(1/3)/[(1/2)+(1/3)+(1/9)]=(6/17) its clear?its ok?

third son
(1/9)/[(1/2)+(1/3)+(1/9)]=(2/17) its clear?its ok?

now (9/17)+(6/17)+(2/17)=1

first son takes 9
second son takes 6
third son takes 2

its clear? its ok?