6/2(1+2)

6/2(1+2), or more properly represented as 6÷2(1+2) = 3 x 3 = 9

because, as brackets play a higher priority then multiplication, the brackets should be simplified first

6 / 2(3)

as 2(3) is no longer strictly a "bracket" in BODMAS, instead being shorthand for 2 x 3, the equation can hence be broken down to

6 / 2 x 3

in which, when on one line, follows BODMAS to be

(6 ÷ 3) x 3, since in BODMAS, division has the same priority has multiplication, only having a higher priority in the case as the division is in front of the multiplication.

Therefore
6 ÷ 2(1+2) resolves to 3 x 3 which is
9.

The question is meant and designed to successfully trick you to thinking that it's

⁶⁄₂₍₁₊₂₎

as the 2(1+2) part and the fraction sign (/) hints so, however the reality is, is that the equation is on one line, and that the fraction symbol is another way of writing the division symbol (÷)... (6÷2)(1+2) == 6÷2(1+2)

THERE IS NO NUMERATOR OR DENOMINATOR SINCE THE ARITHMETIC EXPRESSION IS NOT A FRACTION, IT IS MERELY A MISREPRESENTED DIVISION.
AS A RESULT, THE ENTIRE EXPRESSION CANNOT BE EXPRESSED AS A RATIO
(since it's not a fraction)

THE BRACKETS CAN BE EXPANDED, HOWEVER THE 6÷2 PART MUST BE SIMPLIFIED FIRST TO BE EXPANDED, e.g:

6 divided by 2 (1+2)
means
(6 / 2) * (1+2)

Which is equal to 3(1+2)
Which is 3*1+3*2
Which is 3+6
Which is 9..

Sources

http://www.mathway.com/answer.aspx?p=basi?p=6SMB142(1+2)?p=2?p=?p=?p=?p=?p=0?p=?p=0?p=?p=?p=Simplify
http://www.wolframalpha.com/input/?i=6%C3%B72%281%2B2%29

Also,

2(1+2) ÷ 6 = 1, which is also equal to (2(1+2)) ÷ 6

Whilst:
6÷2 x (1+2), and 6÷2(1+2) [both equal to 9] is NOT 6 ÷ (2(1+2))
as the BODMAS rule would be incorrect if this wasn't the case

Tl;dr

9