To solve this problem, we will first simplify the expressions within the parentheses, and then perform the addition and subtraction as per the given operations.

4/5 (6/7 - 5/4) + 6/5 (5/6 - 4/7)

= 4/5 (24/28 - 35/28) + 6/5 (35/42 - 24/42)

= 4/5 (-11/28) + 6/5 (11/42)

= -44/140 + 66/140

= 22/140

= 11/70

Therefore, 4/5 (6/7 - 5/4) + 6/5 (5/6 - 4/7) simplifies to 11/70.