Simplify the following.
​$$\frac{1}{\frac12+\frac13+\frac16÷(\frac34-\frac13)}$$​​

Correct option is C

​$$\frac{1}{\frac12+\frac13+\frac16÷(\frac34-\frac13)}\\\ \\\implies\frac{1}{\frac12+\frac13+\frac16÷(\frac{9-4}{12})}\\\ \\\implies\frac{1}{\frac12+\frac13+\frac16÷(\frac{5}{12})}\\\ \\\implies\frac{1}{\frac12+\frac13+\frac16÷(\frac{12}{5})}\\\ \\\implies\frac{1}{\frac12+\frac13+\frac25}\\\ \\\implies\frac{1}{\frac{15+10+12}{30}}\\\ \\\implies\frac{1}{\frac{37}{30}}\\\ \\\implies \frac{30}{37}$$​​