To simplify the expression, we can start by simplifying the fractions within the parentheses:

13/8 - 7/9 = (13*9 - 7*8)/(8*9) = (117 - 56)/72 = 61/72

3/7 - 8/15 = (3*15 - 8*7)/(7*15) = (45 - 56)/105 = -11/105

Now we can substitute these simplified fractions back into the original expression:

A = 3/7 * (61/72) - 5/3 * (-11/105)

To multiply fractions, we multiply the numerators together and the denominators together:

A = (3 * 61)/(7 * 72) - (5 * -11)/(3 * 105)

A = 183/504 - (-55/315)

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 504 and 315 is 504:

A = (183 * 315)/(504 * 315) - (-55 * 504)/(315 * 504)

A = 57495/158760 + 27720/158760

Now that we have a common denominator, we can add the fractions:

A = (57495 + 27720)/158760

A = 85215/158760

The fraction 85215/158760 cannot be simplified any further, so that is the final answer.