The value of  $$\frac{2}{3} + \frac{1}{1 + \frac{4}{5}} - \frac{5}{6}$$​ is:

Correct option is C

Given : 

$$\frac{2}{3} + \frac{1}{1 + \frac{4}{5}} - \frac{5}{6}$$​

Solution:

$$1 + \frac{4}5 = \frac{5}5 + \frac{4}5 = \frac{9}5$$​

$$\frac{1} { \frac{9}{5}} = \frac{5}9$$   

Now, 

$$=\frac{2}{3} + \frac{5}{9} - \frac{5}{6}$$  

​$$= \frac{12}{18} + \frac{10}{18} - \frac{15}{18} = \frac{7}{18}$$​​