Rút gọn biểu thức sau đây

To solve these expressions, we need to simplify each fraction separately and then perform the operations.

For the first expression:
(-2/3 + 3/7) : 4/5 + (-1/3 + 4/7) : 4/5

To add or subtract fractions, we need a common denominator. The common denominator for 3 and 7 is 21.
(-2/3 + 3/7) = (-14/21 + 9/21) = -5/21

(-1/3 + 4/7) = (-7/21 + 12/21) = 5/21

Now we can substitute these values back into the expression:
(-5/21) : 4/5 + (5/21) : 4/5

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(-5/21) * (5/4) + (5/21) * (5/4)

Simplifying each fraction:
(-25/84) + (25/84)

Now we can add the fractions:
(-25/84) + (25/84) = 0

Therefore, the value of the first expression is 0.

For the second expression:
(1 3/7 - 5/12) : 4/5 - (3/7 - 17/12) : 4/5

To subtract mixed numbers, we need to convert them to improper fractions.
1 3/7 = (7/7 * 1) + 3/7 = 7/7 + 3/7 = 10/7

(1 3/7 - 5/12) = (10/7 - 5/12)

To subtract fractions, we need a common denominator. The common denominator for 7 and 12 is 84.
(10/7 - 5/12) = (120/84 - 35/84) = 85/84

(3/7 - 17/12) = (36/84 - 119/84) = -83/84

Now we can substitute these values back into the expression:
(85/84) : 4/5 - (-83/84) : 4/5

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(85/84) * (5/4) - (-83/84) * (5/4)

Simplifying each fraction:
(425/336) - (415/336)

Now we can subtract the fractions:
(425/336) - (415/336) = 10/336 = 5/168

Therefore, the value of the second expression is 5/168.