To simplify the expression (-3/4 + 5/13) . 7/2 - (9/4 - 8/13) . 7/2, we can start by simplifying each term separately.

First, let's simplify (-3/4 + 5/13):
To add these fractions, we need to find a common denominator. The least common multiple of 4 and 13 is 52.
(-3/4) * (13/13) + (5/13) * (4/4) = -39/52 + 20/52 = (-39 + 20)/52 = -19/52

Next, let's simplify (9/4 - 8/13):
To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 13 is 52.
(9/4) * (13/13) - (8/13) * (4/4) = 117/52 - 32/52 = (117 - 32)/52 = 85/52

Now, let's substitute these simplified fractions back into the original expression:
(-19/52) * (7/2) - (85/52) * (7/2)

To multiply fractions, we simply multiply the numerators together and the denominators together:
(-19 * 7) / (52 * 2) - (85 * 7) / (52 * 2)

Simplifying further:
-133/104 - 595/104

To subtract fractions, we need to find a common denominator, which is already 104 in this case:
(-133 - 595) / 104

Simplifying further:
-728/104

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 8:
(-728/8) / (104/8) = -91/13

Therefore, the simplified expression is -91/13.