We need to simplify the expression by first converting all the fractions to a common denominator.
4/21 + (13/4 - 11/12) - 5/14 + 2/3
To find the common denominator, we can use the least common multiple of the denominators: 21, 4, 12, and 14, which is 84.
So, we can rewrite the expression with a common denominator of 84:
(16/84) + ((273/84) - (77/84)) - (30/84) + (56/84)
Now we can simplify:
16/84 + (273/84 - 77/84) - 30/84 + 56/8416/84 + (196/84) - 30/84 + 56/8416/84 + 196/84 - 30/84 + 56/84(16 + 196 - 30 + 56)/84238/84119/42
Therefore, the simplified expression is 119/42.
We need to simplify the expression by first converting all the fractions to a common denominator.
4/21 + (13/4 - 11/12) - 5/14 + 2/3
To find the common denominator, we can use the least common multiple of the denominators: 21, 4, 12, and 14, which is 84.
So, we can rewrite the expression with a common denominator of 84:
(16/84) + ((273/84) - (77/84)) - (30/84) + (56/84)
Now we can simplify:
16/84 + (273/84 - 77/84) - 30/84 + 56/84
16/84 + (196/84) - 30/84 + 56/84
16/84 + 196/84 - 30/84 + 56/84
(16 + 196 - 30 + 56)/84
238/84
119/42
Therefore, the simplified expression is 119/42.