Simplify the following.

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

Correct option is C

Given:

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

​​Solution:

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

= $$\frac{1}{2 - \frac{1}{5+\frac{1}{\frac{30-2}{5}}}}$$​​

= $$\frac{1}{2 - \frac{1}{5+\frac{5}{28}}}$$​​

= $$\frac{1}{2 - \frac{1}{\frac{140+5}{28}}}$$​​

= $$\frac{1}{2 - \frac{28}{145}}$$​​

= $$\frac{1}{ \frac{290-28}{145}}$$​

= $$\frac{1}{ \frac{262}{145}}$$​

= $$\frac{145}{262}$$​​