To solve this expression, we need to follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) moving from left to right:
First, let's simplify the addition and subtraction of the mixed numbers:
To solve this expression, we need to follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) moving from left to right:
First, let's simplify the addition and subtraction of the mixed numbers:
2 12/17 + 1 5/17 = 3 + 17/17 + 5/17 = 3 + 22/17 = 4 5/17
3 4/5 + 1 3/5 = 4 + 5/5 + 3/5 = 4 + 8/5 = 5 3/5
Now we substitute the simplified values back into the original expression:
(4 5/17) - (5 3/5) ÷ 6
Now, let's divide the second fraction by 6:
5 3/5 ÷ 6 = 5 + 3/5 ÷ 6 = 5 + 1/5 = 5 1/5
Finally, we can subtract the two mixed numbers:
4 5/17 - 5 1/5 = 4 - 5 - 1/5 + 5/5 = -1 - 1/5 + 1 = -1 4/5
Therefore, the final answer is -1 4/5.