We will start by simplifying the expression inside the parenthesis first.
3\(\frac{1}{2}\) + 4\(\frac{1}{3}\) = (7/2) + (13/3)
To add these two fractions, we need a common denominator. Multiplying the denominators together gives us 6, so:
(7/2) + (13/3) = (21/6) + (26/6) = 47/6
Now, let's simplify the expression in the denominator:
\(\frac{5}{6} - \frac{2}{3}\) = \(\frac{5}{6} - \frac{4}{6}\) = \(\frac{1}{6}\)
Finally, we can substitute these values into the original expression:
(3\(\frac{1}{2}\) + 4\(\frac{1}{3}\)) ÷ (\(\frac{5}{6}\) - \(\frac{2}{3}\)) = (47/6) ÷ (1/6)
When dividing fractions, we can multiply the first fraction by the reciprocal of the second:
(47/6) ÷ (1/6) = (47/6) x (6/1) = 47
Therefore, the answer is 47.