To simplify the expression, we need to find a common denominator for both fractions in the numerator and the denominator.

For the numerator:
The common denominator for 6, 39, and 51 is 6 * 39 * 51 = 11934.
So, we can rewrite 1/6 as (1/6) * (1989/1989) = 1989/11934.
Similarly, we can rewrite 1/39 as (1/39) * (306/306) = 306/11934.
And we can rewrite 1/51 as (1/51) * (234/234) = 234/11934.

Now, the numerator becomes 1989/11934 - 306/11934 + 234/11934.

For the denominator:
The common denominator for 8, 52, and 68 is 8 * 52 * 68 = 35328.
So, we can rewrite 1/8 as (1/8) * (4416/4416) = 4416/35328.
Similarly, we can rewrite 1/52 as (1/52) * (676/676) = 676/35328.
And we can rewrite 1/68 as (1/68) * (408/408) = 408/35328.

Now, the denominator becomes 4416/35328 - 676/35328 + 408/35328.

Combining the numerators and denominators, we have:

(1989/11934 - 306/11934 + 234/11934) / (4416/35328 - 676/35328 + 408/35328).

Simplifying the numerator:
1989 - 306 + 234 = 1917.

Simplifying the denominator:
4416 - 676 + 408 = 4148.

Therefore, the simplified expression is:

1917/4148.